Hybrid Composite Wires for Tensile Armour in Flexible Risers

Transcription

1 Hybrid Composite Wires for Tensile Armour in Flexible Risers A thesis submitted to The University of Manchester for the degree of Doctorate of Philosophy In the faculty of Science and Engineering September 2016 Mayank Gautam Textile Composite Group School of Materials

2 Table of Contents Table of Contents Table of Contents... 1 List of Figures... 6 List of Tables Thesis Abstract Declaration Copyright Statement Acknowledgements Introduction Introduction to flexible risers Research motivations and rationale Hybrid composite wires Research disseminations Outline of the thesis Review of Literature Flexible risers Types of risers Composition of flexible riser Carcass Pressure sheath Pressure armour Tensile armour

3 Table of Contents Anti-wear layers Anti-buckling layer and outer sheath Carbon steel Design process for flexible risers Failure modes in flexible risers Failure modes of flexible riser due to tensile armours Defects due to manufacturing processes Tensile fatigue Buckling Composites Unidirectional composite manufacturing: pultrusion Composites in marine applications Composites in risers Braiding Braid geometric and structural parameters Braid angle and braid cover Braid crimp Braid topology Mechanical properties of braid (non-infused state) Braidtrusion Summary Study of Manufacturing Processes for Hybrid Wire Composite Wires Material specification and properties Quality of composite rods Manufacturing process for hybrid composite wire

4 Table of Contents Over-braiding process: Pack with Ф 2 mm rods Over-braiding process: Pack with Ф 4 mm rods Measurement process: Braid structural parameters Braid angle Braid thickness Tow width Braid crimp Results: Braid parameters Theoretical and experimental braid cover factor Quantification of the tow tension during the braiding process Summary Mechanical Testing and Characterisation of Hybrid Composite Wires Mechanical tests procedures Flexure tests Torsion tests Tensile tests for single rods Mechanical characterisation Axial and in-plane shear modulus of single rods Flexural behaviour Effect of point load Effect of boundary conditions Torsional behaviour Comparison of hybrid composite wires with traditional metallic armour wires Corrosion

5 Table of Contents Flexural and torsional stiffness Comparison with traditional metallic tensile armour wires Comparison with metallic structures with similar dimensions Behaviour under through thickness compression Summary Multi-scale Modelling of Hybrid Composite Armour Wires Introduction Methodology for multiscale modelling Elastic properties of composite rods Braid shell properties: meso-mechanical analytical model Computational modelling: finite element model Geometry and mesh Mesh sensitivity study Interaction properties Boundary conditions Results and observations Torsional behaviour Flexural behaviour Summary Parametric Studies Using Multiscale Model Introduction Effect of friction Effect of model length Different combinations of material systems Summary

6 Table of Contents Conclusions and Directions for Future Research Manufacturing study Mechanical characterisation Multi-scale model and parametric studies Recommendations for future work Bibliography Appendix Word Count: 45,235 5

7 List of Figures List of Figures Figure 1.1: Comparison between two flexible risers with (a) metallic tensile armour wires, and (b) hybrid composite tensile armour wire Figure 1.2: Different configurations of hybrid wires studied in thesis Figure 1.3: Conceptual representation of types of tensile armour wires: (a) traditional carbon steel, (b) line packed circular composite rods held together by over-braid sleeve, (c) carbon reinforced composite strip, (d) carbon reinforced composite strips stacked in the form of packed cards held together by over-braid sleeve, and (e) hexagonal packed circular composite rods held together by over-braid sleeve (studied in this thesis) Figure 1.4: Schematic representation of the outline of thesis Figure 2.1: Carcass of a flexible riser [15] Figure 2.2: Zeta interlock layer for pressure armour [16] Figure 2.3: Composition of a typical flexible riser Figure 2.4: Fabrication process of tensile armour [13, 22] Figure 2.5: Failure of flexible risers due to: (a) failure of external sheath [22] (b) collapse of carcass [13] Figure 2.6: Failure of flexible risers due to corrosion of tensile armour wires from H2S and CO2 [22, 35] Figure 2.7: Failure of tensile armour wires due to tensile fatigue [39], Figure 2.8: Failure of tensile armour wires due to radial buckling [45] Figure 2.9: Failure of tensile armour wires due to lateral buckling [47] Figure 2.10: Schematic representation of a unidirectional fibre reinforced composite with a: (a) 3-D view and (b) 2-D cross-sectional view Figure 2.11 : Molecular structure of ethylene and of ultra-high molecular-weight polyethylene (UHMW-PE), where n is the degree of polymerization Figure 2.12: Molecular chain distribution of: (a) thermoplastic polymer, and (b) thermoset polymer obtained from [61] Figure 2.13: Typical pultrusion machine obtained from [70]

8 List of Figures Figure 2.14: Flexible riser with (a) steel armour, and (b) composite armour shown in [80] Figure 2.15: Schematic representation of parts of a maypole braiding machine: (a) deck, (b) carrier with mounted bobbin Figure 2.16: Computer aided drawing using TexGen software [89] of a braid with 45⁰ braid angle depicting: (a) braid angle, (b) braid unit cell, and (c) braid crimp Figure 2.17: Most commonly used braid topologies: (a) Diamond (1/1), (b) Regular (2/2), and (c) Hercules (3/3) Figure 2.18: A typical load extension curve of a biaxial braided structure [103] Figure 2.19 : Arrangement of braiding-pultrusion process obtained from [105] Figure 3.1: Process of measurement of density of composite rod in (a) & (b), and braid fibres in (c) & (d) Figure 3.2: Scanning electron micro-graphs of cross-section of Ф 4 mm rod Figure 3.3: Optical micrographs showing alignment of fibres along the length of pultruded composite rods with (a) & (b) Ф 2 mm, and (c) & (d) Ф 4 mm Figure 3.4: Different configurations of hybrid composite tensile armour wires Note - HCW: Hybrid composite wires; θ is the braid angle Figure 3.5: Hybrid composite tensile armour wire manufacturing processes Figure 3.6: Reverse braiding and braid jamming phenomenon Figure 3.7: Braiding at low carrier tension of only 50 grams Figure 3.8: Braid angle measurement through: (a) digital protractor and (b) image analysis Figure 3.9: Process of braid thickeness measurement using: (a) circumference of the hybrid composite wires and (b) thickness of hybrid composite wires Figure 3.10: Schematic of cross-section of hybrid composite wire showing different thicknesses of components Figure 3.11: Process of measurement of tow width using image analysis software.. 72 Figure 3.12: Schematic representation of the crimp determination process Figure 3.13: Theoretical and experimental cover factor for hybrid armour wires with Ф 4 mm rods, using 12 carriers on a 24 carrier braiding machine (containing the images of the hybrid wires)

9 List of Figures Figure 3.14: 2-D Schematic representation of tension mechanism during braiding process using just two carriers Figure 3.15: Schematic representation of different cases of tow tension that may be encountered during the braiding process Figure 3.16: Schematic representation of methodology used for calculating coefficient of friction using braid carriers Figure 4.1: Flexural tests being conducted on hybrid composite wire using: (a) three point flexural test (for hybrid wires with Φ 2 mm rods), (b) four point flexural test (for hybrid wires with Φ 2 mm rods), (c) three point flexural test (for hybrid wires with Φ 4 mm rods), and (d) four point flexural test (for hybrid wires with Φ 4 mm rods) Figure 4.2: Torsion test to maximum limit of 40 twist angle for: (a) hybrid wire (45 braid angle) with Ф 2 mm rods and (b) hybrid wire (45 braid angle) with Ф 4 mm rods Figure 4.3: Four point flexural test on hybrid composite wires (with Ф 4 mm rods and regular braid topology) for: (a) 30 and (b) 45 braid angle Figure 4.4: Failed single rods during flexural test for (a) Ф 2 mm rod, (b) 4 mm diameter rod, (c) micrograph of the cross-section of fractured Ф 4 mm rod, at the point loads Figure 4.5: Flexural behaviour of hybrid wires and individual rods for: (a) Ф 2 mm rods and (b) Ф 4 mm rods Figure 4.6: Effect of edge boundary conditions Figure 4.7: Effect of boundary condition for hybrid wire with Ф 4 mm rods: (a) without braid (taped edges), (b) without braid (bonded edges), (c) with braid (45, 2/2, taped edges), and (d) with braid (45, 2/2, non-bonded edges) Figure 4.8: Torsional behaviour of hybrid wires and individual rods for: (a) Ф 2 mm rods and (b) Ф 4 mm rods Figure 4.9: Comparison between different structures using: (a) flexural rigidity and (b) torsional rigidity Figure 5.1: Schematic representation of the process for multi-scale modelling of hybrid composite armour wires Figure 5.2: Schematic representation of material coordinates of pultruded composite rods, with fibre axis as 1 direction

10 List of Figures Figure 5.3: (a) Material orientation for composite rod, (b) material orientation for shell, and (c) mesh for the model Figure 5.4: The different number of elements used to carry out the mesh sensitivity study on multiscale model for hybrid composite wires with Ф 4 mm rods Figure 5.5: Mesh density sensitivity study for flexural and torsional mode of deformation for hybrid wire assembly with Ф 4 mm rods Figure 5.6: Micrographs of cross-section of composite rod with Ф 4 mm, showing matrix rich circumference Figure 5.7: Hoop pressure (po) applied on the braid shell, and (b) displacements (in mm) encountered by rods due to applied hoop pressure Figure 5.8: Schematic representation of boundary conditions on the multi-scale model in case of: (a) torsion, (b) three-point flexure, and (c) four-point flexure tests Figure 5.9: Experimental and FE behaviour of hybrid composite wires under torsion Figure 5.10: Stress (von Misses in Nmm -2 ) distribution in multiscale model for 45 braid with diamond braid topology at 3 /m twist: (a) without hoop pressure, and (b) with hoop pressure. Note: SNEG (fraction = -1) implies stresses at face of shell in contact the rods Figure 5.11: Experimental and FE behaviour of hybrid composite wires for 3 point flexural test Figure 5.12: Stress (von Misses in Nmm -2 ) distribution in multiscale model for 45 braid with diamond braid topology at a mid-span deflection of 2.5 mm, in a 3 point flexural set-up, (a) without hoop pressure and (b) with hoop pressure. Note: SNEG (fraction = -1) implies stresses at face of shell in contact the rod Figure 5.13: Experimental and FE behaviour of hybrid composite wires for 4 point flexural test Figure 5.14: Stress (von Misses in Nmm -2 ) distribution in multiscale model for 45 braid with diamond braid at a mid-span deflection of ~2.5 mm, in a 4 point flexural set-up: (a) without hoop pressure, and (b) with hoop pressure. Note: SNEG (fraction = -1) implies stresses at face of shell in contact the rods Figure 6.1: Effect of coefficient of friction in hybrid composite wires using multiscale model

11 List of Figures Figure 6.2: Effect of length in hybrid composite wires using multiscale model Figure 6.3: Torsional rigidities of hybrid composite material with different combination of material system using multi-scale model Figure 6.4: Flexural rigidities of hybrid composite material with different combination of material system using multi-scale model

12 List of Tables List of Tables Table 2.1: Failure modes of flexible risers obtained from [33] Table 3.1: Structural properties of braids Table 3.2: Tow tensions for different braid configuration (T0 = 1.5 N) Table 4.1: Material properties determined experimentally (for composite rods), and from manufacturer s technical data sheet and literature (for braid fibres) Table 4.2 : Flexural rigidities for all tested specimen Table 4.3 : Torsional rigidities for all tested specimen Table 5.1: Elastic properties of fibre and matrix in the composite rod found from literature [with references] Table 5.2: Elastic properties of composite rods Table 5.3: The properties UHMW-PE fibres and HD-PE matrix Table 5.4: Calculated properties of UHMW-PE tow Table 5.5: Elastic properties of different configurations of braid shell in hybrid composite wire with Ф 4 mm rods, using analytical model Table 5.6: Hoop pressure values for different braid configuration Table 6.1: Properties of different fibres and matrix systems obtained from literature [with references] Table 6.2: Properties of different composite rods Table 6.3: Properties of different braid tows Table 6.4: Properties of different braid shell

13 Thesis Abstract Thesis Abstract Flexible risers that carry hydrocarbon fuels from the subsea facilities to the floatation units above the sea surface are composed of multiple metallic and polymeric layers (in their wall). Among these layers, the tensile armour layer consists of several helically wound metallic wires; these tensile armour layers carry the weight of the riser, provide tensile stiffness & strength and maintain the structural integrity of the riser structure during harsh underwater currents. However, as the oil & gas fields in shallow waters are receding, the oil & gas industry is being forced to move towards deeper offshore waters, where the metallic tensile armour wires pose limitations (fatigue, corrosion, weight, etc.). The study presented in this thesis introduces: a novel tensile armour wire which comprises of hexagonal packed seven circular carbon & vinyl-ester pultruded composite rods, held together by an over-braid sleeve of Dyneema fibres. The resultant structure can provide equivalent tensile strength as compared to traditional armour wires, yet be highly complaint in flexure and torsion; additionally it exhibits excellent corrosion resistance and fatigue life which carbon reinforced composites and Dyneema fibres are known to display. Through mechanical tests conducted in this research, it has been found that the flexural and torsional behaviour of hybrid composite wires can be tailored depending upon the riser curvature, by simply changing the structural and geometrical parameters (rod diameter, braid angle and braid topology) during the manufacturing stage. The effect of end boundary conditions on flexural performance of the hybrid composite wires has also been investigated in this thesis. Both pultrusion and braiding processes can help in continuous production of hybrid composite wires. A multiscale model has been developed using analytical and computational approach for the hybrid composite wires, to further understand their mechanical behaviour and of their constituents. The friction between different components has been incorporated into the model, and the equivalent hoop pressure exerted by the braid tows on bundled rods, due to pre-tension in these tows (due to braiding), also has been taken into account. The multi-scale model has been validated for different configurations of these wires, providing good agreement with mechanical test results. The validated model has been used further to conduct a series of parametric studies: one of these parametric studies, helped to understand the effect on torsional and flexural behaviour of these wires by varying the values of coefficient of friction between the different components in these wires. The other study involved: studying the effect of varying the model length, to determine the ideal length to thickness ratio for mechanical testing (torsion and flexure); additionally the effect of using different material systems for composite rods and the braid in hybrid composite wires has been studied using parametric study through multi-scale model. 12

14 Declaration Declaration No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning. 13

15 Copyright Statement Copyright Statement i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright ) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trademarks and other intellectual property (the Intellectual Property ) and any reproductions of copyright works in the thesis, for example graphs and tables ( Reproductions ), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property University IP Policy (see in any relevant Thesis restriction declarations deposited in the University Library, The University Library s regulations (see and in The University s policy on Presentation of Theses 14

16 Acknowledgements Acknowledgements I want to dedicate this thesis to my parents and my late grandparents. I would also like to give a special thanks to my younger brother, who is has always been immensely supportive. I would like use this opportunity to thank my PhD supervisor: Prof Prasad Potluri, for believing I could research on this topic, and being a great mentor. I have truly learnt a lot from him, and cannot thank him enough for all his support. I am extremely fortunate to have had him as my research supervisor. I also would like to thank Dr. Kali-babu Katnam, also my PhD supervisor, for teaching me what effective research and writing is. Also I would like to thank him giving me conceptual understanding of Solid Mechanics. I am extremely fortunate to also have had him as my research supervisor, and it has always been a great pleasure working with him. I also would like to express my gratitude towards GE Oil & Gas (Newcastle upon Tyne, UK), for funding my PhD and providing all the financial support needed for this project. I want to thank Dr. Vineet Jha (GE Oil & Gas), for being my industrial supervisor for this project, and providing me with any help I needed. I also want thank my colleagues: Dr. Shankhachur Roy (who taught me how to braid), Dr. Sabahat Nawaz, Dr. Dhaval Jetavat, Mr. Kinjalkumar Patel, Dr. Dhavalkumar Patel, Dr. Vivek Koncherry, and Dr. Zeeshan Yousaf. All these people have been a family and great support system during my PhD. I also want to extend my gratitude towards: Dr. Richard Kennon, Mr. Thomas Kerr, Dr. Alan Nesbitt, Mrs. Olwen Ritchard, Mr. Bill Godwin, Mr. Christopher Cowan, and Mr. Roy Conway for all their help. 15

17 Introduction Introduction T his thesis introduces a novel designed tensile armour wire for flexible risers, in form of a flexible hybrid composite, to help overcome the current limitations of flexible risers due to the existing metallic tensile armour wires. In this chapter, a brief introduction about the flexible risers will be given, and their limitations due to metallic tensile armour wires will be highlighted. The need and advantages for hybrid composite wires will be put forward Introduction to flexible risers Flexible risers help in transportation of hydrocarbon fuels from the subsea facilities to the floatation units above the sea surface and have typical diameter of 12. There has been a rapid increase in use of flexible risers, since past decades, due to their easier transportation from the offshore production facilities to the target fields and their reusability. The wall of a flexible riser (also referred to as the annulus) consists of several layers of metallic and polymeric bands, and extruded polymer layers. These non-bonded materials (forming concentric layers) in the annulus of the riser result in a hybrid composite structure that imparts the riser, flexural & torsional compliance and high tensile stiffness & strength, helping in maintaining the structural integrity of the riser during rough under-water currents. Among several layers that constitute the annulus of a flexible riser (shown in Figure 1.1a), the tensile armour layer is of great importance. The tensile armour is made from metallic (generally carbon steel) bands that are wound helically into the flexible riser. A typical flexible riser may consist of two to four cross-wound tensile armour wires. A tensile armour layer in flexible riser helps in maintaining high tensile stiffness and strength of the flexible riser. As the riser is suspended from the floatation units above the sea surface to the subsea units, it needs to be under high tension or else the riser will undergo axial compression leading to buckling of tensile armour wires; the tensile 16

18 Introduction armour layer also helps the riser in countering flexural and torsional deformation loads arising from continuous under-water currents. The tensile armour in short carries the weight of the riser and helps in maintaining its overall structural integrity Research motivations and rationale With the passage of time as the number of available oil and gas reservoirs in shallow waters are decreasing, the need for the offshore oil & gas industry to move towards deeper under-water reservoirs is rising. Although the flexible risers have found success in operation in shallow waters, the operation in deeper waters (> 2.4 km) poses limitations. With an increase in depth, the hydrostatic external pressure acting on the riser also increases, adding to the weight of these risers. The high hydrostatic pressures can induce high radial compressive forces on the risers that could lead to radial buckling of tensile armour wires (phenomenon also known as bird-caging). An increase in riser weight due to increase in depth, causes extreme tensile loads and drag forces that can ultimately lead to tensile fatigue of tensile armour wires at both the ends of the riser. As the oil & gas industry aims to move towards deeper offshore fields, there is also a need for larger diameter flexible risers, in order to increase transportation capacity and productivity. An increase in riser diameter would however, result in addition of more material, further adding to its weight, which increases as the water depth increases. Recently in 2014, Petrobras has successfully made flexible risers operational at the deepest recorded depth of 2.2 km for oil extraction [1], and before that, a depth of 1.9 km was achieved in 2012 [2]. The limitation of both these flexible risers is the reduction in size (diameter < 7.5 ). As the sea depths increase, the salinity of waters also increases and so does the presence of corrosive gasses, such as hydrogen disulphide and carbon dioxide deposited in deeper sea beds. Corrosion due to high water salinity and corrosive gases is another big limitation of metallic layers in flexible riser. These corrosive gases can easily seep through annulus of a riser through a small damage in carcass (inner most 17

19 Introduction layer of riser) or, externally if the external sheath is damaged, leading to rapid corrosion of the tensile and pressure armours, and the carcass. Hence, due to these limitations (weight, buckling, fatigue, and corrosions) of the tensile armour wires there is a need for an alternative, which is capable of overcoming majority of these problems Hybrid composite wires Fibre reinforced polymer composites are now finding increasing use in flexible risers. Recent works [3-6] have shown great potential for carbon fibre thermoplastic and thermoset matrix composites in replacing metallic tensile and hoop armours. These composites show higher tensile strength and fatigue, excellent corrosion resistance, and enable significant overall weight reduction of flexible riser systems. However, for tensile armour, continuous manufacturing processes to produce the materials in the required long helices are not very well developed. Subsequently, initial applications have involved the use of rectangular cross-section carbon reinforced composite wires. These wires under higher flexure and torsion, impose high strains on the composite wire, limiting their usable thickness and resistance to brittle damage/fracture. Although the use of composites as tensile armour wires is still being developed, there are a range of offshore oil & gas applications already employing composites: manufacturing of rigid risers, tethers, floors and platforms for above sea facilities, casings, J-tubes etc. [7]. The alternate to metallic tensile armour wires proposed in this thesis is in the form of a hybrid composite wire, produced using a combination of pultrusion and braiding processes. While pultrusion is a continuous unidirectional composite forming technique, braiding is a textile forming technique that is capable of producing tubular (and flat) near net shaped fabrics. These hybrid composite wires are produced by stacking seven circular pultruded composite rods (with unidirectional fibres and polymer matrix) in form of hexagonal pack, followed by an over-braiding process. The structure of these wires is inspired from the structure of flexible riser itself, consisting of multiple non-bonded components that form a composite structure with 18

20 Introduction high tensile stiffness, yet maintaining high flexural and torsional compliance. A schematic representation of how the hybrid composite tensile armour wires would look in a flexible riser has been shown in Figure 1.1b. Traditional (metallic) tensile armour Hybrid composite wires in tensile armour (a) (b) Figure 1.1: Comparison between two flexible risers with (a) metallic tensile armour wires, and (b) hybrid composite tensile armour wire There are several advantages of using hybrid composite armour wires. The prime among them is the tailorability of their mechanical properties. The flexural and torsional rigidities of these wires can be varied during the manufacturing stage by changing the structural parameters such as composite rod diameter, braid angle, and braid topology (different configurations of hybrid composite wires studied in this thesis are shown in Figure 1.2). As the composite rod bundle and the over-braid sleeve, are not bonded in nature at high deformations the rods can slide over one another helping in absorbing impacts due to high deformation loads. Both pultrusion and braiding processes can be incorporated in assembly line to help in continuous production of these tensile armour wires. The process of winding could have been replaced by braiding, but the filament wound sleeve will not be as stable as a braid sleeve, where the tows are interlaced providing stability to the braid sleeve. 19

21 Introduction HCW with Φ 4 mm rods and 2/2 braid HCW with Φ 4 mm rods and 1/1 braid HCW with Φ 2 mm rods and 1/1 braid Note - HCW: Hybrid composite wires; θ is the braid angle Figure 1.2: Different configurations of hybrid wires studied in thesis There could be other possibilities (shown in Figure 1.3) of producing hybrid composite wires: one with the same composite rods arranged in a line and then be over-braided, and the other by stacking rectangular composite strips over one-another (in form of packed cards) and then overbraiding them. Both of these possible structures will produce a similar cross-sectional geometry (rectangular) as the traditional metallic armour wires. But both these possibilities have lesser advantages when compared with hybrid composite wires produced using hexagonal packed composite rods, and held by over-braid sleeve. The line packed rods with an over-braid sleeve will be an unstable structure, and will not be able to wind successfully into the riser, unlike hexagonal packed rods that are highly stable even at very high flexural and torsional deformations. In the second possibility, which contains the rectangular composite strip, which is already in commercial use and limited to very low curvature risers, there will be large surface area of contact between the stacked composite strips that could cause serious abrasions and erosion of matrix rich layer (found in pultruded composites) exposing fibres and causing filamentation, at high flexural deflections and twists, in comparison with hexagonal packed rods that only have line contact between them. 20

22 Introduction (a) (b) (c) (d) (e) Figure 1.3: Conceptual representation of types of tensile armour wires: (a) traditional carbon steel, (b) line packed circular composite rods held together by over-braid sleeve, (c) carbon reinforced composite strip, (d) carbon reinforced composite strips stacked in the form of packed cards held together by over-braid sleeve, and (e) hexagonal packed circular composite rods held together by over-braid sleeve (studied in this thesis) Hence, the structure of hybrid composite wires with hexagonally packed rods held together with an over-braid sleeve is a good choice, as an alternative to metallic tensile armour wires, and has been studied in detail in this thesis. The structure of hybrid composite wires, is patented (pending) by GE Oil & Gas, Newcastle upon Tyne, UK Research disseminations Several portions of study conducted in this thesis have been published in the following journals: Gautam M, Potluri P, Katnam KB, Jha V, Leyland J, Latto J, & Dodds, N. Hybrid composite wires for tensile armours in flexible risers: Manufacturing and mechanical characterisation. Composite Structures. 2016; 150: Gautam M, Katnam KB, Potluri P, Jha V, Dodds N, & Latto J, Hybrid Composite Tensile Armour Wires in Flexible Risers: A Multi-scale Model. Composite Structures. 2016; 162:

23 Introduction Some portions of study conducted in this thesis were also presented in the following conference: Gautam M, Potluri P, Katnam KB, Jha V, Leyland J. Hybrid composite tensile armour wires for flexible risers: A multi-scale model. In: 2nd International Conference on Mechanics of Composites. Porto (Portugal), July Outline of the thesis Introduction to flexible risers and need for hybrid composite wires Review of literature Manufacturing study of hybrid composite wires Mechanical characterisation of hybrid composite wires Multi-scale modelling of hybrid composite wires Parametric study using multi-scale modelling technique Thesis conclusion and recommendation for future work Figure 1.4: Schematic representation of the outline of thesis The basic outline of this thesis has been shown in Figure 1.4. In this chapter, a brief introduction to flexible risers was given, and their limitations due to tensile armour wires were highlighted. The need and advantages for hybrid composite wires as an alternative to metallic tensile armour wires were put forward. In the following chapter (Chapter 2) a detailed review of literature in reference to flexible risers, composites in offshore industry, pultrusion and braiding process has been conducted. 22

24 Introduction In Chapter 3, a detailed study of the manufacturing processes involved in production of the hybrid composite wires has been conducted. This will be followed by Chapter 4, where mechanical characterisation in form of flexural and torsional behaviour of hybrid composite wires, and the single rods used in their packing, has been carried out. The performance of hybrid composite wires with their metallic counterparts has also been reported. The chapter (Chapter 5) following this will describe the multi-scale modelling technique used for finite element modelling of elastic behaviour (flexural and torsional) of hybrid composite wires. After validating the multi-scale model with experimental behaviour, a detailed parametric study has been conducted in Chapter 6, to further understand the mechanical behaviour of these wires. Following this chapter (Chapter 7), the study conducted in the thesis will be concluded and recommendations for future research work will be proposed. 23

25 Review of Literature Review of Literature A comprehensive review of literature with reference to the subject of research has been conducted in this chapter. The literature review has been divided into four sections, the first section will describe the composite structure of flexible risers, and the problems associated with traditional tensile armour wires. The second section will describe composite materials, pultrusion process and the range of applications where composites are being used in marine & offshore industry, especially in flexible risers. The third section will give an in-depth review of braiding and different terminologies associated with it (braid geometrical and structural parameters) that would be helpful in understanding the trends (mechanical) and observations in further chapters. The fourth section would explain a process that is combination of braiding and pultrusion Flexible risers Flexible risers are capable of operating at sea depths of 8,000 feet (2.4 km), with high pressures of 10,000 psi (~ 70 MPa), and temperatures above 65.5º C (150 F), accompanied by large amount of vessel motions in challenging weather conditions. A flexible riser can have several functions which include: transportation of well products, carry well control lines, injection of fluids and export of processed products [8], from the sea bed to the floating production units above the sea surface. The materials transported through the flexible risers can be (or both) corrosive and hot, typically comprising of high-pressure mixtures of hydrocarbon liquids/gases, water and solids [9]. Flexible risers are composite structures that are highly compliant in flexure, but stiff in response to internal/external pressures, torque and tension [10]. The compliance in flexure mode is achieved, due to the ability of multiple layers, in riser annulus to slide over each other, during a riser movement. A flexible riser is produced using metallic (carbon steel) armour layers with high axial stiffness and high tensile strength (~1500 MPa), and polymeric sheaths with low axial stiffness, which are used primarily as 24

26 Review of Literature sealants, and layer separators. This combination of metallic armours and polymeric sheaths helps flexible riser impart a number of advantages over other types of pipelines and risers which include the ability to vary fabrication processes depending upon type of fluid being transported and service environments, convenience of storing (the risers can be wound on creels), reduced transport and installation costs, and the ability to couple with compliant structures subsea [11]. The multiple layers in a flexible riser provides flexibility, as mentioned before, and helps the riser designer to design a riser with a higher allowable curvature [12]. The manufacturing of all non-bonded flexible pipes is done in a few highly specialised and equipped sites. These sites have specialised equipment and machinery for both winding of the different metallic layers and the polymer extrusion; these sites also contain specialized areas for mounting the end fittings, test facilities, handling, and storage [13] Types of risers Risers can be divided into flexible and rigid, where flexible risers offer greater advantages as compared to rigid risers, since they can be easily transported in form of large creels, whereas rigid risers comprising of rigid tubes are difficult to transport. The flexible risers also require less installation time and are capable of adapting in changing field environment offering a more economical solution. The flexible risers can be classified in offshore industry as: bonded and non-bonded. In the bonded flexible risers, different layers of polymer and steel layers are bonded together by the application of heat and pressure (vulcanization) process, and are produced form a single construction [9]. Bonded flexible risers pipes are mostly used in short sections such as jumpers [11]. On the other hand, non-bonded flexible pipes which constitute a vast majority of flexible risers employed, are manufactured for more dynamic applications, and are produced in lengths ranging between several hundred meters and have separate steel and plastic layers which are free slide over to each other [9], that overall imparts higher flexural compliance in comparison with bonded flexible risers. Flexible risers depict non-linear behaviour due to the coupling 25

27 Review of Literature between axial, torsional and flexural deformations [7]. The non-linearity is caused due to multiple layered annulus of the flexible riser. The polymeric layers introduce material non-linearity while the helical configuration of the metallic wires introduces geometric non-linearity. The non-linear behaviour is further pronounced from interlayer interactions caused due to the slippage of layers and the changing contact conditions due to deformations Composition of flexible riser The different layers in a flexible riser and the role of each layer in the flexible riser have been described in Figure 2.3. The different layers in a typical flexible riser from inwards out comprises of carcass, pressure sheath, pressure armour, anti-buckling tapes, tensile armour, sealant tape and outer sheath Carcass The carcass is the inner most layer in a flexible riser, which comprises of an interlocked metallic strip (shown in Figure 2.1). The main functions of carcass is to prevent the pipe from being crushed under the external pressure [14], and also act as an abrasion cover for the rest of the layers, and prevent them to come in contact with the bore (cavity) fluids. The carcass is the only metallic layer in contact with fluids inside the bore. Figure 2.1: Carcass of a flexible riser [15] The type of material used to make the carcass, comprise of stainless steel, but this material can depend on the type of fluids (hot or corrosive) being transported through the carcass, and the ability to withstand forces during riser operation [11]. The cylindrical structure of the carcass helps in providing the strength and stiffness along 26

28 Review of Literature the radial (hoop or circumferential) direction, adding flexural compliance [16], with help of interlock structure, as a result of which the strips can slide over each other during high flexural deformations Pressure sheath As the carcass is not leak proof, the pressure sheath layer is applied to maintain the bore fluid integrity and prevent fluids from flowing freely into the pipe annulus [16]. The most commonly used materials for manufacturing the pressure sheaths are high density poly-ethylene (HDPE), cross linked poly-ethylene (XLPE), nylon 11, nylon 12, and poly-vinylidene fluoride (PVDF) due to their good ageing behaviour, excellent resistance to acids, seawater and oil [17] Pressure armour The pressure armour as the name suggests helps to provide resistance against hoop stresses, which arise as a result of internal pressures. The pressure armour layer has an interlocking profile, as shown in Figure 2.2, which is similar to the structure of the carcass, produced from rolled carbon steel with tensile strength ranging between 700 MPa and 900 MPa [16]. The pressure armour is most commonly produced using Z- shaped steel wires wound at angles close to (but not) 90⁰ (hoop wound), which supports the system internal pressure and also radial inward forces [18]. Figure 2.2: Zeta interlock layer for pressure armour [16] 27

29 Review of Literature Figure 2.3: Composition of a typical flexible riser 28

30 Review of Literature Tensile armour The tensile armour layer carries the gravitational weight of the carcass, when suspended from the floatation units above sea towards the extraction units on sea bed. The tensile armour relies naturally on the interfacial transfer of axial tensile loads through interfacial shear forces [19]. Like the carcass and the pressure armour, the tensile armour wires, are also produced using carbon steel. The fabrication process of tensile armour has been shown in Figure Anti-wear layers When the flexible riser comprising of two to four cross-wound metallic tensile armour layers and pressure armour layer, is subjected to cyclic bending, these layers will slide over one another, which is essential for flexural compliance but would lead to abrasion between the wires in these armours. In order to avoid the abrasion and wear of the armour wires, anti-wear tape layers are applied between each of the armour layers. The anti-wear tape is not leak-proof, and fluids in the annulus (region between the carcass and the outer sheath) can flow through this tape layer [20]. The materials used for anti-wear layers are similar to materials used for pressure sheaths Anti-buckling layer and outer sheath The anti-buckling layer in a flexible riser helps in preventing radial and lateral buckling of tensile armour wires that are common causes of failure of tensile armours. The radial and lateral buckling phenomenon has been described in detail in the following sections (Page 35). The outer polymer sheath in flexible risers eliminates requirement for cathodic protection (protection of a metal structure from corrosion due to water by making it act as an electrical cathode), which promotes reliability and maintenance expenses of the pipe [21]. The outer sheath is produced by extrusion process, unlike anti-buckling tapes that are wound onto the tensile armour. The outer sheath is made using thermoplastic polymers that are made from nylon-11 or are PVDF polymers. 29

31 Review of Literature (a) (b) Fabrication of carcass layer with help of interlocked S shaped metallic strips (c) Fabrication of pressure armour by hoop winding (lay angle of 90, with respect to riser axis) of metallic strips (d) Fabrication of tensile armour by helical winding of metallic strips Application of anti-buckling tape on the outer most layer of tensile armour (e) Production of outer sheath of flexible riser with help of pultrusion process using thermoplastic polymers Figure 2.4: Fabrication process of tensile armour [13, 22] 30

32 Review of Literature Carbon steel Steel is one of the most widely used alloys, due to its malleability and high strength. All forms of steel contain carbon, since steel is an alloy of carbon and iron. Carbon steel is has been described by the American Iron and Steel Institute as a form of steel that has no minimum specified content of cobalt, molybdenum, nickel, chromium, tungsten, zirconium, or vanadium or specified requirement for any other element to be added specifically to obtain a desired alloying effect [23]. The most important factor in determining the properties of carbon steel is the carbon content; higher content carbon increases the tensile strength, increases hardness, reduces malleability, and weldability [24]. The different forms of carbon steel with low, medium and high carbon content have been described in [25]: low carbon steel have carbon content of 0.06 to 0.25%, resulting in lowest toughness and lowest tensile strength among different types of carbon steels; this form of steel is used for manufacturing rivets, shafts, and pressed products. The medium carbon steel contains has carbon content between 0.25% and 0.6%, resulting in higher tensile strength and rigidity as compared to low carbon steel finding application in producing gears, and machine parts. The high carbon steel has carbon content between 0.6% and 1.5%, resulting in highest tensile strength among different forms of carbon steel. This form of steel is primarily used in cutting tools. Carbon steel that is used in multiple layers in a flexible riser can also be classified depending upon the rolling process during its manufacturing process as, hot rolled and cold rolled steel. While hot rolled steel is produced at temperatures higher than recrystallization temperature of steel, cold rolled steel is produced at room temperatures [26]. The major disadvantage of hot rolling is that the steel work pieces when hot can undergo oxidation at their surfaces, and lose some plasticity. The surface finish is poor due to which an additional process acid treatment has to be applied [27]. The hot rolled steel can be more malleable than cold rolled steel and can be formed into any shape however, as the steel cools down the dimensions change due to which cold rolled steel is preferred when precise dimensions are required. The cold rolled steel has higher strength as compared to hot rolled steel due to strain hardening during 31

33 Review of Literature rolling process [28]. The type of carbon steel used in flexible risers consists of a high carbon steel (due to higher strength) which is cold rolled (precise dimensions) [29]. The primary function of steel in a flexible riser is to provide hoop strength (carcass and pressure armour) and tensile strength (tensile armours). The high strain to failure helps in imparting ductility to overall structure resulting in lower safety factor. The secondary functions of steel elements in riser, is to impart resistance to wear and fatigue, and corrosion resistance (limited). However, the disadvantages of carbon steel, leading to failures in flexible risers are discussed in the following sections Design process for flexible risers The key point when designing a flexible riser is to maintain its structural integrity. The detailed requirements for the riser such as: size (length and diameter), pressure rating and internal coatings are dependent upon the service conditions and installation processes involves [8]. The standards that govern the design, fabrication, installation and operation of flexible risers and pipes, are as per the American Petroleum Institute standards: 17B [30] and 17J [31]. The design of the riser system has been explained in [32], where it has been called as an iterative process, which primarily involves riser configuration assumption and analysis Failure modes in flexible risers Failure of a riser during service implies loss of ability to transport products safely and effectively. A failure in flexible riser can be catastrophic (i.e. when the riser ruptures), or minor uncontrolled loss of the riser integrity or blockage in the pipe [33]. There are high number of potential failure modes that can occur due to the composite structure of a flexible riser, however the number of different failure modes experienced in operation is more limited [34]. The failure modes of a flexible riser have been depicted in Table 2.1, where the most probable failure modes and defects for a flexible riser, as mentioned in API 17B RP [30], have been tabulated, and have been found to be due to tensile armour layer. 32

34 Review of Literature (a) (b) Figure 2.5: Failure of flexible risers due to: (a) failure of external sheath [22] (b) collapse of carcass [13] Some common causes of leading to failure of a flexible riser include collapse of carcass (shown in Figure 2.6a), which occurs when the pressure sheath fails and the external pressure far exceeds the internal pressure. The pressure armour can also lead to failure of flexible riser during service and installation operations, due to high flexure curvatures, which can lead to unlocking of the pressure armour wires. The unlocking of pressure armour wires can progress gradually and damage large sections of the riser, causing loss of its structural integrity. The failure modes caused due to tensile armour wires has been described in detail in the following section. The abrasion between the flexible risers (when wrapped around creels for transportation or when they are in service), and the through thickness failures of external sheath are some common causes of riser failure initiations [13], however, if through thickness is small and develop only closer to the riser ends, it may not affect the overall integrity of the riser. However, if the outer sheath of a flexible riser is severely damaged, the seawater can permeate inwards, towards the tensile armour wires, further into inner layers. If during this time, the gases from the fluids being transferred permeate through the pressure barrier and diffuse with sea water, a corrosive environment can be created. 33

35 Review of Literature Figure 2.6: Failure of flexible risers due to corrosion of tensile armour wires from H 2 S and CO 2 [22, 35] The carbon steel has poor resistance towards both (hydrogen di-sulphide) H 2 S or (carbon di-oxide) CO 2 gases which can easily diffuse into sea water. Even small traces of H 2 S is detrimental for very high strength carbon steels [36]. Often due to condensation water forms between the layers of the flexible riser, which again when comes in contact with H 2 S or CO 2, can initiate corrosion process. In such a scenario, the strength of steel is often compromised, especially during sour conditions (high levels of corrosive gasses), by using lower content carbon steel [37], reducing the performance of the flexible riser. 34

36 Review of Literature Table 2.1: Failure modes of flexible risers obtained from [33] Type Failure Mode Description 1 Collapse Collapse of carcass and / or pressure armour due to excessive tension, excessive pressure or installation overloads. 2 Over Bending Rupture or crack of external or internal sheets. 3 Erosion Erosion of internal carcass 4 Compressive failure Birdcaging of tensile armour wires 5 Tensile failure Rupture of tensile armours due to excess tension 6 Torsional Failure Failure of tensile armour 7 Fatigue failure Tensile armour wire fatigue 8 Burst Rupture of tensile or pressure armours due to excess internal pressure 9 Corrosion Corrosion of internal carcass or tensile/pressure armour exposed to sea water or diffused product Failure modes of flexible riser due to tensile armours Defects due to manufacturing processes The manufacturing process of tensile armour wires results in developing hard and textured microstructure, which is prone to the occurrence of small marks and pits, are formed due to cold rolling manufacturing process of carbon steel [38]. These marks can cause crack development, which can result in rapid progressive failure that can significantly shorten the life of the component [39]. Moreover, they are capable of tearing off of the softer layers (polymeric layers), that may result in consequent leakage of the internal products [30], that may compromise the overall structural integrity of the riser. 35

37 Review of Literature Tensile fatigue The main failure mode of flexible risers, when operating in deep waters, occurs at the riser s top section, closer to end fitting, due to the tensile fatigue in tensile armour wires (shown in Figure 2.7). However, the failure of flexible riser only occurs when there is significant rupture of tensile armour wires, which is why the structural integrity of a riser-end fitting connection is assessed by monitoring the rupture of these wires [40]. The rupture of tensile armour wires closer to the end fittings is because the tensile armour wires are subjected to stresses equivalent to 30-50% of their yield strength [41]. Rupture of these wires can cause structural instability and re-balancing of loads, which can lead to an increase in load and friction between the unbroken wires and debris [42]. Figure 2.7: Failure of tensile armour wires due to tensile fatigue [39], It has been observed from periodic inspection of flexible risers, that the top sections of the risers are capable of compromising structural integrity of the riser as whole, by possibly triggering failure mechanisms, which majorly comprise of damage in outer sheath, torsional instability and fatigue damage of tensile armour wires, of which major of these flaws generally originate during installation or, more frequently, during operation due to contact with another riser or the platform structure [33, 41, 43]. 36

38 Review of Literature Buckling Buckling of tensile armours is a mode of failure caused due to axial compressive stresses in the armour wires, primarily due to the external pressure in deeper waters. These external pressures, can lead to instabilities in radial and lateral direction causing severe structural damage and leakages in the pipe [44]. This section reports two common types of buckling occurring in tensile armour wires: radial buckling and lateral buckling of tensile armour wires. Figure 2.8: Failure of tensile armour wires due to radial buckling [45] Radial buckling of the tensile armour wires is a well-known failure mode for the flexible risers, and it is often referred to as "bird caging", caused due to the failure of supporting anti-buckling layer and elastic buckling of metallic tensile armour wires. The failure of anti-buckling layer, occurs when the stresses in the anti-buckling layer exceed its ultimate strengths, causing expansion of tensile armour wires in radial direction [12]. The buckling caused due to high axial compression on the flexible pipe leads also leads to instability in the tensile armour wires, causing them to deflect in the radial direction creating the classical "bird-cage" [45] as can be seen in Figure

39 Review of Literature The preventive measures to avoid radial buckling has been reported in [46], where the primary measure stated, is that to avoid riser configurations that can lead to excessive compression; an additional support for the wires may be added by applying high strength tapes around the armour layers to avoid failure of anti-buckling layer. Birdcaging can also occur from torsional failure if the forces acting on the riser are large enough, which can be avoided by reducing torsional loads or the torsional capacity, achieved by increasing the lay angle of the wires or addition of extra tensile armour wires [17]. Figure 2.9: Failure of tensile armour wires due to lateral buckling [47]. Another type of buckling that occurs in flexible risers is lateral buckling. This form of buckling is caused during installation of the flexible risers, but may also occur if the floating production unit is temporarily shut down [48]. The cause of this type of buckling the flexible pipe has been referred in [49] as End Cap Effect, occurring when the pipe is in free-hanging position from an installation vessel to the seabed. This can lead to repeated bending cycles, due to the wave loads and vessel movements occurring mostly when the riser is empty during installation, which can lead to compression due to hydrostatic pressure on the end cap of an empty pipe. This hydrostatic pressure can produce a true-wall compression component acting on the pipe, imposing a danger to the structural integrity of a riser, especially when the outer sheath (a polymeric layer) is damaged. Both radial and lateral buckling of tensile armour wires can be reduced by using the same lay angles and same direction of lay 38

40 Review of Literature for anti-buckling tape as the outer (final layer) tensile armour [50], and by increasing the cross-wound layers, these however lead to added production time and cost Composites A composite can be defined as a material system of two or more constituents combined heterogeneously, exhibiting superior desired properties (primarily mechanical) than their individual constituent would exhibit independently. In a fibre reinforced polymer composite, that has been used to produce the hybrid composite wires, there are two types of constituents, comprising of fibres which act as reinforcement and the polymer matrix (continuous phase), which helps to bind the fibres together. The matrix helps in locking the fibres in a particular orientation or location inside the composite. The fibre reinforced composite can be divided on the basis of size, geometry and the orientation of reinforced fibre location into particulate, short fibre and long fibre composites. Matrix Fibre (a) (b) Figure 2.10: Schematic representation of a unidirectional fibre reinforced composite with a: (a) 3-D view and (b) 2-D cross-sectional view The particulate composites comprise of particles of varying shapes and sizes in matrix medium (e.g. carbon nano-tubes dispersed in a matrix system), while the short fibre composites comprise of the short fibres either randomly distributed or unidirectional placed in the matrix system. The long fibre composites comprise of: unidirectional composites, cross-ply laminates or textile composites, and multiaxial composites. On the basis the type of matrix, the fibre reinforced composites can be divided into polymer matrix (e.g. fibres in a thermoset or thermoplastic polymer), metal matrix (e.g. fibres in an aluminium matrix), and ceramic matrix (e.g. fibres in a silicon carbide). 39

41 Review of Literature The fibres that act as reinforcements in a composite can be broadly classified as natural (cotton, linen, flax, jute, wool, etc.) and synthetic fibres (carbon, glass, Dyneema, aramids, etc.). The synthetic fibres, are higher performance fibres in comparison with natural fibres, and are known for their unique physical (higher axial or shear strength and stiffness) and chemical properties (fire retardance, chemical or corrosion resistance) that are unique to these fibres. Each of the high performance fibre, have a combination of these unique properties that acquire a niche place in the fibre spectrum. Carbon, glass and aramid (Kevlar) fibres are one of the most commonly used high performance fibres in composite industry. The glass fibres (produced using melt spinning) are the most commonly used fibres, in low to medium performance composites because of their high tensile strength and lower cost of production, whilst aramid fibres are used where higher stiffness are required with lower density and higher moisture absorption. Carbon fibres, that have been incorporated in the unidirectional composite rods for the study of hybrid composite wires, are composed almost entirely of carbon atoms and possess extremely high tensile modulus and strength with lower densities as compared to glass and aramid fibres [51]. Due to their high strength to weight ratios, they find extensive use in aerospace grade composites [52, 53]. Majority of carbon fibres are derived from poly-acrylonitrile (PAN) based copolymer. The primary reason for major use of PAN to produce carbon fibres, is that the PAN polymer does not melt, but has the ability to get dissolved in suitable solvents [54]. Moreover, the PAN precursors can be solution-spun into thin fibres that can be thermally processed into inelastic fibres by thermal treatment between C because to obtain carbon fibres [55]. Ultra-high molecular weight polyethylene (UHMW-PE) fibres, commercially known as Dyneema, are another class of high performance of fibres that have been used in the braiding process for production of hybrid composite armour wires. These fibres consist of long-chain polyolefin with a molar mass between 3 million and 5 million with tensile strength is reported to be approximately 40% greater than poly-phenylene terephthalamides (Kevlar and Twaron) fibres [56]. Polyethylene has no functional groups as depicted in Figure 2.11, resulting in superior chemical resistance as 40

42 Review of Literature compared to other materials [57]. The UHMW-PE fibres are obtained from gel spinning process. In this process, very long molecules are dissolved in a volatile solvent and spun through a spinneret, where the molecular chains get disentangled and remain so after cooling in gel-like filaments and as the fibre is drawn, near perfect macromolecular orientation is attained [8]. Figure 2.11 : Molecular structure of ethylene and of ultra-high molecular-weight polyethylene (UHMW-PE), where n is the degree of polymerization These fibres have high crystallinity of about 85% which gives them a unique property of high specific modulus, lower elongation and lower fibre density [58], making them useful in weight-sensitive applications like towing lines, helmet reinforcement or sails. Due to their lower density than water (~ 0.97 g/cm 3 ), they are widely used by marine industry, for towing and salvage operations moreover, as the fibre diameter is not affected by winches, it is also used in ship mooring [59]. The UHMW-PE fibres also have excellent wear resistance and low coefficient of friction values [60] making them to be used extensively in manufacturing of high performance ropes. The resins that form of key constituent of fibre reinforced polymer composites can be classified on the basis of their response to temperature as thermoplastic or thermoset. Thermoset and thermoplastic polymers exhibit the same general behaviour except at high temperatures, the thermoplastic polymers melt, whilst thermoset polymers do not. The thermoplastic polymers are semi-crystalline in nature, containing both crystalline and amorphous regions, where the molecular chains in amorphous regions are completely random in contrast with its crystalline region where they are highly ordered (as depicted in Figure 2.12) [61]. They are also susceptible to high creep. On the contrary, thermoset polymers are highly cross-linked polymers, due to which they 41

43 Review of Literature cannot be melted at high temperatures, however the higher temperatures can cause the average distance between the molecular chains to increase, leading to stiffness degradation. If the temperatures are exceedingly high, the molecular backbone of the polymer might rupture causing chemical degradation of the polymer. In thermoset polymers, the cross-linking of polymers occurs due to the presence of a macromolecule, consisting of covalently bonded repeating units formed during polymerisation process. In thermoplastic polymers, since the molecular chains are not cross-linked, the chains can orient and flow freely at higher temperatures, allowing the polymer to melt [62]. Crystalline region Cross-linking of molecules Amorphous region (a) (b) Figure 2.12: Molecular chain distribution of: (a) thermoplastic polymer, and (b) thermoset polymer obtained from [61] The most common thermoset polymer resins include: unsaturated poly-ester, epoxy, vinyl-ester, poly-urethanes, and phenols. Unsaturated poly-ester resins are mostly used for glass fibre reinforced composites, due to their lower costs and good mechanical properties [63]. Epoxies, on the other hand are more expensive than polyester resins, but have superior mechanical properties and good resistance to alkaline conditions, they are also the most widely used matrix for carbon fibre reinforced composites [64]. Vinyl-esters that form the polymer matrix part of composite rods used in manufacturing of hybrid composite wires were developed to combine the advantages of epoxy resins with the better handling and faster cure which are typical for unsaturated polyester resins. High mechanical properties are obtained without 42

44 Review of Literature complex processing and handling that are typical in case of epoxy resin systems [65]. Due to the their ease of processing, good mechanical properties and corrosion resistance, vinyl-ester resin systems are used widely in structural engineering applications [66]. Other resin systems like polyurethanes, are elastic polymers that have low mechanical strength and poor thermal stability [67]. Phenolic resins are relatively cheap in comparison with other polymer resins, and have good resistance to high temperatures and resistance to acids and smoke [68], but the manufacturing method (condensation system) used to produce this resin system created voids in its structure, resulting in lower mechanical properties among all thermoset resins [64]. Thermoplastic polymers are used mostly for short fibre composites [69], but are now also being used to produce long continuous fibre reinforced composites. Some examples of thermoplastic polymers include: poly-ether-ether ketone, poly-ethylene, poly-propylene, and poly-vinyl-chloride Unidirectional composite manufacturing: pultrusion Figure 2.13: Typical pultrusion machine obtained from [70] The pultrusion process is a cost effective automated process for manufacturing continuous, constant cross-section composite profiles [71]. The solid pultruded fibre reinforced composite rods have been used to produce hybrid composite wires for tensile armour in flexible risers. A schematic representation of the pultrusion process has been shown in Figure The basic principle of a pultrusion involves, feeding continuous fibre strands through a guiding system before these fibres are impregnated with the desired liquid matrix. Following this step, the reinforced wet fibres are 43

45 Review of Literature gathered and progressed into the required preformed shape (in case of hybrid composite wire: circular) which closely matches the desired finished profile, prior to entering the heated die to cure. As the impregnated bundle of fibres exits from the die in form of a fully shaped solid structure, it is then passed through the reciprocating pullers and then cut using a diamond saw. The cut profiles are then loaded off using a take-up device that runs at constant speed Composites in marine applications The composites have been finding an increasing use in range of marine applications in recent decades, especially in the production of high speed yachts and racing boats, with an increase in use of carbon fibre reinforced polymer composites, providing 20% to 50% reduction in weight and yet still maintaining high stiffness and improving impact resistance [72]. The use composites is also spread into the production of military submarine and naval ships, due to their high strength to weight ratio, low density and good resistance to marine environment [73]. Composites are also finding an increasing use for offshore application in the oil and gas industry, where they are now being used extensively in the manufacturing of platforms over sea (floors and walls), and in production of pipes, tanks and vessels for both onshore and offshore platforms [74] Composites in risers The use of composites in risers was first reported for rigid risers, as the flexible risers came into use much later. Some of the initial works reported in literature was by Ahlstone in 1973 [75], who developed glass reinforced epoxy polymer tubular composites produced using filament wound technique. Later carbon based reinforced polymer tubular composites were also developed [76]. Jha et al. (2015) [6], have recently introduced fibre reinforced composite pressure armour to replace the traditional metallic pressure armour in flexible risers, using carbon fibre reinforced poly-vinyldene thermoplastic polymer composite. 44

46 Review of Literature The use of composite materials as tensile armour wires in non-bonded flexible risers was first suggested by Lotveit & Ward (1991) [77], suggesting aramid fibres as an alternate reinforce material, due to its superior strength to weight ratio. However the corrosion resistance of aramid fibres which is poor to medium also needs to be taken into consideration. The first non-bonded flexible riser with tensile composite armour wire was manufactured by Coflexip Stena Offshore in 1993 [78], using glass fibre reinforced epoxy composites, the riser was reported to be much lighter than the traditional non-bonded flexible riser. Kalman et al. in 1996 [79], presented a light weight design which incorporated carbon fibre and thermoplastic polymer composite strip (rectangular cross-section) to replace the steel tensile armour wires. A weight reduction of 30% was achieved for the riser designed to meet the same performance requirements. Their further work in [4] showed the tensile fatigue behaviour of carbon fibre tensile armour to be promising since, some of the fatigue tests carried out until 20 millions of cycles without failure at more than 50% of ultimate tensile strength. Carbon steel tensile armour wires Carbon-fibre reinforced polymer composite tensile armour wires (a) (b) Figure 2.14: Flexible riser with (a) steel armour, and (b) composite armour shown in [80] 45

47 Review of Literature Soon after, Do et al (2003) in [80], used carbon fibre based composite strips (rectangular cross-section) as tensile armour wires, and concluded that mechanical properties of these wires were not affected by the content of H 2 S or CO 2 (corrosive environments), they also concluded that since, these wires are elastic in nature, bending of these wires is easier than carbon steel wires, simplifying the armour operation process. However, the curvature limit of these wires needed to be kept into consideration. If the Figure 2.14 seen, which shows a flexible riser with both metallic and composite tensile armour, the composite armour is cross-wound twice (for same carcass diameter) since the thickness of the composite strips used is much lesser and limited due to curvature limit (as mentioned above). The cost of producing a composite tensile armour riser is higher than carbon steel flexible riser however, the total cost saving related with lighter weight riser is expected to be sufficient in comparison with its higher cost of production [81]. In addition to their light weight, their excellent corrosion resistance, and tensile fatigue further adds to their advantage over metallic wires Braiding Braids can be identified as two dimensional (2D) or three dimensional (3D). The principle difference between a 2D braid and a 3D braid is the through thickness interlacement which is not present in a 2D braid. Three-dimensional (3D) braiding technology is an extension of two-dimensional (2D) braiding technology in which the fabric is constructed by intertwining or orthogonal interlacing of three or more yarns to form an integral structure through position displacement [82]. In comparison with weaving which is another textile forming technique that uses interlacement of yarns or tows, braiding can have higher production rates when producing tubular structures or flat structures (with narrow width). Unlike weaving where only orthogonal interlacement is possible, braiding can produced interlacement angles ranging between 0 and 90 (except these two angles which would imply no interlacement), where different angles have different mechanical properties. Braiding machines are also easier to set up in comparison with weaving looms. The ease of setting up also 46

48 Review of Literature facilitates, different fibres can be used at the same time, in order to produce hybrid structures highlight advantages in comparison with weaving. There are different types of braiding machines that can be employed, however maypole type braiding machines are among most commonly used, and have been incorporated in production of hybrid composite wires. The deck of a maypole braider typically comprises of two flat metallic plates, bolted together. The upper plate consists of tracks in form of rose curve or in form of serpentine tracks, while the bottom plate does not comprise of any tracks. The horngears are assembled so that the slots in the top flange coincide at the intersections in tracking and when a carrier reaches a track intersection, it is forced by the shape of the track to transfer from one horngear the next, this transfer process forms the principle working of the braiding process [83]. (a) (b) Figure 2.15: Schematic representation of parts of a maypole braiding machine: (a) deck, (b) carrier with mounted bobbin 47

49 Review of Literature There are several types of braid carriers, however the basic intended function is to regulate the tension during the braiding mechanism, in addition of controlling tension magnitudes and providing constant tension are also desirable features of the carriers [84]. An ideal carrier tensioning system, it is expected the material would release yet keeping the tension within a small range about the desired tension level [85]. Take-up mechanism that is manual, semi-automated, or fully automated, needs to make sure that the braid is drawn smoothly and at a precise uniform rate, in order to produce a high quality braid. A slight jerk induced by take-up device can loosen the braid and conversely a pause can cause braid distortion. It was concluded from the study conducted on braided ropes in [86] that at constant braid angles, when the take-up rate is increased, the corresponding tenacity of the braided structure also increases; in the experiments performed, high take-up rate provided 13-28% higher yield tenacity values than the low take-up rate for each pattern for both diamond (1/1) and regular (2/2) braid Braid geometric and structural parameters The braid geometrical (braid angle, braid cover and braid topology) and structural (braid crimp and braid tow dimensions), are described in this section; these parameters have been used extensively in further chapters to help understand the mechanical behaviour of hybrid composite wires both experimentally and through computation modelling Braid angle and braid cover The braid angle, as depicted in Figure 2.16, can be described as the angle subtended by the interlaced yarns or tows (strand of multiple untwisted filaments) with the braid axis (vertical axis). The braid angle (θ) has been mathematically determined in [87] with the help radius of the mandrel/core (R) it is braided on, rotational machine speed (ω) and take up speed (v) as depicted in Eq. (2.1). By varying any one of three factors and keeping the other two constant, in Eq. (2.1), the braid angle can be varied. However, this equation is applicable to only circular cross-section and may be 48

50 Review of Literature modified for different geometrical cross-section (only regular cross-section). The minimum and maximum braid angles are limited by the phenomenon of jamming, which is related to the maximum shear distortion that can be put on a fabric [88]. The braid angle can only be varied between 0⁰ and 90⁰, excluding 0⁰ and 90⁰ which would imply no interlacement of tows or yarns. (a) (b) (c) Figure 2.16: Computer aided drawing using TexGen software [89] of a braid with 45⁰ braid angle depicting: (a) braid angle, (b) braid unit cell, and (c) braid crimp The braid angle has the ability to increase and decrease when the braid sleeve is not secured on the mandrel/core surface. While braiding a smaller braid angle, the convergence length is higher conversely convergence length is lower and closer to the machine when during higher braid angles. Convergence length is the horizontal distance between the point of stable braid formation and plane of the braid ring. θ = tan -1 ( Rω v ) (2.1) The coverage of the braided yarns or tows on the surface they are braided on, can be quantified in terms of cover factor (Cf), which has been described in [90] as, the ratio of the yarn- occupied area within a unit cell to the area of the unit cell. The braid angle accompanied by mandrel diameter, number of carriers used and the yarn width, have a significant effect upon the braid coverage, according to Eq. (2.2), presented in [91]. In this equation, Wy width of the yarn, Nc is number of carrier employed during braiding, R is the radius of the cylindrical mandrel/core and θ is the braid angle. The 49

51 Review of Literature equation is however, only applicable for circular cross-section and can be modified depending upon the geometrical cross-section. C f = area (ABCD) area (A B C D ) area (ABCD) = 1 - ( 1 2 W y N c 4πrcosθ ) (2.2) The cover factor gives a good indication of the fibre percentage per unit cell of the fabric. A cover factor of 1 would imply full braid cover and cover factor closer to 0 would imply least coverage. According to Eq. (2.2), an increase in the width of yarn or tow, or an increase in the number of carriers employed, would lead to an increase in the braid cover. However, if mandrel diameter/core is increased, keeping all other factors constant, the braid cover will reduce due to an increase in the surface area. The work conducted in [90] concluded that, keeping all factors constant in Eq. (2.2), as the braid angle is increased between 0⁰ to 90⁰, the cover factor decreases till 45⁰, beyond which it starts to increase. The braid angle is a major contributing factor when designing braids, as it has a pivotal impact on the mechanical properties of the resultant structure. The study conducted in [92] on braids, found that as the specimen with largest number of tows and largest braid angle depicted maximum extensibility moreover, as with same number of tows, as the braid angle increases the load of rupture also increases. It was also concluded that braid fabrication method can produce strands with elasticity 5 to 10 times higher than the unidirectional fibres. Work conducted in [93], on braided elastic core, also concluded a decrease in tensile strength with an increase in braid angle. The effect of braid angle in case of composites is also quite significant. An increase in braid angle leads to a decrease in axial modulus (with reference to braid axis) and an increase in axial strain [94-96], and an increase in transverse stiffness [97]. As the braid angle increases the in-plane shear modulus increases till 45⁰, after which the in-plane shear stiffness decreases [98]. 50

52 Review of Literature Braid crimp One of the earliest works on braid crimp includes work by Brunnschweiler [99], quantifying the crimp of braided structures using Eq. (2.3), as the difference in length between the actual length of a yarn or tow (Lc) and the length of its projection on the braid (Lnc), expressed as a ratio of the latter length. However, this definition assumes that the yarn or tow is of quasi-elliptical cross-sections, inextensible, incompressible and flexible (bending and wrapping). The crimp can also be described in terms of crimp angle, which is the largest rotation of the yarn or tow, from the horizontal plane [100], implying greater the crimp angle, greater would be the crimp of the braided structure. C = [(L c L nc )/(L nc )] 100 (2.3) In production of textile fabrics such as braided or woven, the crimp is inevitable as the basic principle of the fabric formation for both weaving and braiding involves interlacement of yarns or tows. When the braid structure is moved between the two extreme angles of 0⁰ and 90, the crimp associated also changes. The value of crimp will be a minimum when the braid angle (θ) is closer to 0 and maximum when θ is closer to 90 moreover, the crimp value will be a minimum at the extended jamming position and a maximum at the contrasted jamming position [90]. The yarn or tow jamming which also contributes towards crimp introduction during the braid manufacturing, occurs due to a high tow deposition per unit area, at a higher braid angle. The jamming position is a point after which the braided fabric can no longer be extended or contracted. As the braid cover increases, the possibility of tow jamming also increases, resulting in increasing the possibility of tow distortion. The work conducted in [90] also shows the effect of cover factor on the crimp of the braid, by assuming the cross-sectional shape of the yarn as elliptical using the mathematical relation established between the yarn spacing and the braid angle in its jammed state. The study concluded, theoretically, a 73% increase in the braid crimp 51

53 Review of Literature when the braid is contracted to its jammed state. A higher crimp has a reducing effect upon the stiffness of the composites (especially in axial direction) [100], as the undulated strands will react to the external force non-uniformly lowering the stiffness of braided composite [101] Braid topology The topology of a braid is dependent upon the number of bobbins and choice of carriers on the braiding machine to be used for braiding. The three most common type of braided structures (shown in Figure 2.17) are diamond, regular, and Hercules braids. If a tow continuously passes over one tow and then under one tow of the opposing group, it is called a 1/1 braid or a diamond braid. Similarly, if a tow continuously passes over two tows and then under two tows of the opposing group, it can be referred to as called a 2/2 braid formation or a regular braid. A 3/3 braid or a Hercules braid is produced when, a strand or a tow continuously passes over three tows and then under tows of the opposing group. (a) (b) (c) Figure 2.17: Most commonly used braid topologies: (a) Diamond (1/1), (b) Regular (2/2), and (c) Hercules (3/3) On a maypole braiding machine with horndogs containing 2 slots, the fully occupied carriers produce regular braid. However, when only alternate carriers are occupied such that one horndog slot is employed, a diamond braid is produced. Other topologies include 2/1 and 3/1, but do not have any specific names [102]. The tenacity values of 2/2 braid is higher than 1/1 braid due to lower number of interlacement points resulting 52

54 Review of Literature in lower level of crimp helping to conclude the effect of braid topology on the tenacity of the resultant braided structure [86] Mechanical properties of braid (non-infused state) There have been several works reported in the literature describing the mechanical properties of biaxial braids [91, 94, 99, 103]. The behaviour of biaxial braid sleeve with higher braid angle subjected to a tensile load has been divided into four zones in [103] (shown in Figure 2.18). In the first zone (OP) the braid does not show considerable response to extension followed by second zone (PQ) where the braid undergoes geometric transition leading to a sharp increase in the stiffness. In the third zone (QR), fibre properties govern the tensile response ultimately leading to the point of braid rupture in the fourth zone (RS). Figure 2.18: A typical load extension curve of a biaxial braided structure [103] However in smaller braid angles the first two zones are shorter as the braid angle is closer to loading direction, which has been experimentally observed in [104]. The mechanical response of biaxial braid sleeve with a core material is different as compared to braid sleeve without sleeve as described above, since the presence of core eliminates the first two zones observed in [103]. 53

55 Review of Literature 2.4. Braidtrusion There have been several works reported in literature with reference to the braid pultrusion process which involves addition of a braiding machine into the first step of pultrusion production line. A simple product of the braiding-pultrusion technique is a braid-pultruded cylindrical rod which is comprised of a braided cover and a core of unidirectional fibres. Figure 2.19 : Arrangement of braiding-pultrusion process obtained from [105] The basic principle of braid-pultrusion process involves, the roving strands to unwound from the bobbins held in the creel and then passing them through an alignment card, where the twist insertion in the roving is prevented and the alignment of the fibres is ensured as they are passed through a resin bath, the aligned fibres are then braided and passed to a secondary resin bath to wet the braided fibres prior to pass them through a heated die where they are cured and then cut off using a diamond point cutter [105]. However, there are other processes where the braiding machine is kept in production line such that the tubular braid is made to pass through a resin injection component or a resin bath followed by a pultrusion component [106]. Ahmadi, et al., [105] have further investigated the effects of braid angle on the performance of the braid-pultruded composite rod by using three different angles of 30, 45 and 55 respectively and observed decrease in the flexural rigidity as the braid angle was increased. It was conculded from their study that the braiding over pultruded rods, causes a drop in the tensile and flexural properties of the structure, however at same time overbraiding enhances the shear modulus of the structure when compared 54

56 Review of Literature with pultruded counterparts of same fibre-volume fraction and rod diameter. The inline braiders however, serve certain distadvantages during maufacturing such that inline braiding can limit the diameter of the resultant tubular braid due to limitting size of the braiding machine involved in production line moreover, the braided subtrates produced from in-line braiding machine limits the process to the speed of braiding considering the speed of pultrusion, in addition there are several quality checks that need to be done on the braided structure which further slow down the process [107]. It should be noted that the process of production of braid-pultruded rods is very different from manufacturing of hybrid composite tensile armour wires which involves manufacturing of pultruded composite rods first and then over-braiding the bundled composite rods. The over-braid sleeve is dry in nature and is not impregnrated with any resin Summary A comprehensive review of literature was carried out in this chapter. The individual role of tensile armour and other layers in flexible risers was described. The failure modes of flexible risers, especially due to tensile armour wires and their limitations constituting of tensile fatigue, corrosion, radial and lateral buckling were high-lighted. The pultrusion and braiding processes, accompanied by a combination of both processes in form of Braidtrusion were described. Different works in context with of fibre reinforced polymer composites in offshore industry especially in flexible risers were reported in this chapter. There have been several works using carbon reinforced composite materials in tensile armour for flexible risers [3, 5], that have proved their excellent corrosion (towards H2S and CO2) and fatigue resistance. However, due to the high strains that are induced in these composite strips if the thickness is increased, can lead to brittle damages when being around into these flexible risers [108]; there thicknesses is currently limited to thinner profiles. 55

57 Review of Literature The limitations of both metallic wires and recently introduced carbon composite wires for tensile armour, clearly indicate the requirement of an alternative, which will be studied extensively in this thesis. 56

58 Study of Manufacturing Processes for Hybrid Wire Composite Wires Study of Manufacturing Processes for Hybrid Wire Composite Wires T his chapter describes the manufacturing process used to produce hybrid composite armour wires for tensile armours. The reason for selecting the braid configurations (braid angle, and braid topologies) studied in this thesis has been described in detail in this chapter. The process of measurement of geometrical and structural parameters for the biaxial over-braid sleeve has been described followed by analysis of the results obtained. The theoretical expression for calculating the cover factor of braid sleeves for hybrid composite wires has been presented with comparisons with experimentally measured values, and theoretical quantification of tension in the braid tows during the braiding will be described in detail in this chapter Material specification and properties The pultruded composite rods with unidirectional carbon fibres & vinyl-ester matrix were used for manufacturing the hybrid composite wires. These composite rods were circular in nature with diameter (Ф) of 2 mm and 4 mm, obtained from Exel Composites (UK). The filament diameter of carbon fibres (T700) in both rods was found to be µm. The fibres used for braiding were Ultra High Molecular Weight Poly-ethylene (SK76) or Dyneema (known commercially) supplied by DSM group. The linear density of the fibre tows was 1760 dtex or 176 tex (tex can be defined as number of grams of fibres in 1 km of tow). There were 780 filaments in a single tow, with each filament having a diameter of 16.1 µm. The density of carbon & vinyl-ester composite rods with Ф 2 mm was found to be 1.53 ± 0.05 gcm -3, and with Ф 4 mm was found to be equal to 1.51 ± 0.01 gcm -3. The density of the fibres for braiding was found to be 0.97 ± 0.01 gcm -3. The density measurement procedure has been shown in Figure 3.1. The density of the composite rods and the braid fibres was measured using Mettler Toledo density measuring device (shown in Figure 3.1). 57

59 Study of Manufacturing Processes for Hybrid Wire Composite Wires (a) Weight of the braid fibres (Dyneema) are first measured in air Weight of the braid fibres (Dyneema) the being measured in water (b) (c) Weight of the composite rod first measured in air Weight of the composite rod then being measured in water (d) Figure 3.1: Process of measurement of density of composite rod in (a) & (b), and braid fibres in (c) & (d) The device uses Archimedes principle to measure the density of materials with high precision (weight measured up to fourth decimal place). The first step involves measurement of weight of the sample in air, and then in water, and then dividing the 58

60 Study of Manufacturing Processes for Hybrid Wire Composite Wires difference in the weight of the solid in water and air with the weight of the solid in air. As observed in Figure 3.1, the shape of the basket in which the specimens are kept in water is different in case of composite rod and braid fibres. For a material having density equal or greater than 1 gcm -3, the convex (with reference to the bottom surface of the beaker containing water) shaped basket is chosen, and for materials with density less than 1 gcm -3, the basket is concave in nature. The material with density less than 1 gcm -3, would float on the surface of water, which is the reason why the basket is concave in nature; the material with density lower than 1 gcm -3 is not allowed to float on the surface of the water due to the concave nature of the basket Quality of composite rods The fibre volume fraction (Vf) for composite rods was determined experimentally using the matrix digestion method as specified in ASTM D3171 [109], quantified to be 0.60 ± for Φ 2 mm rods and 0.61 ± for Φ 4 mm rods. A high void volume fraction found for composite rods, with a value of ± for Φ 2 mm rods, and ± for Φ 4 mm rods, both calculated using Eq. (3.1), obtained from [109], where Vf is the fibre volume fraction and Vm is matrix volume fraction. Damaged fibres Voids Figure 3.2: Scanning electron micro-graphs of cross-section of Ф 4 mm rod 59

61 Study of Manufacturing Processes for Hybrid Wire Composite Wires V v = 1 V m V f (3.1) The presence of voids and the deformed fibres using scanning electron micrographs, in the composite rod have been shown in Figure 3.2. The presence of voids even at a very low fibre volume fraction, can lead to a significant degradation of the composite properties [110]. The alignment of reinforced fibres in the composite rods was observed using optical microscopy and has been shown in Figure 3.3, where missalignment of reinforced fibres can be seen for both diameter rods. This miss-alignment of fibres implies the alignment of fibres along the composite length other than the vertical axis of the composite rods. (a) (b) (c) (d) Figure 3.3: Optical micrographs showing alignment of fibres along the length of pultruded composite rods with (a) & (b) Ф 2 mm, and (c) & (d) Ф 4 mm The defects arising from manufacturing of pultruded composites, such as void and micro-cracks (not observed in composite rods used) are caused due to non-optimal 60

62 Study of Manufacturing Processes for Hybrid Wire Composite Wires curing of composites during pultrusion process, and can affect linear and nonlinear behaviour of pultruded composites [111]. The miss-aligned fibres along the length of composite rods could have arisen due to improper feeding of carbon fibres from the creels. The deformed fibres, could be a result of twisted roving (bundle of multiple tows), being fed into the manufacturing stage. The twisted filaments in composite rods can appear to be in form of deformed fibres when the composite rods are examined along the cross-section Manufacturing process for hybrid composite wire The manufacturing process of hybrid composite tensile armour wires is shown in Figure 3.5. The first step in manufacturing these wires was to wind the required number of bobbins with UHMW-PE fibres, using Herzog automated winder. The wound bobbins were then mounted onto the carriers of braiding machine. Then the unidirectional composite rods with the same diameter (either Φ 2 mm or Φ 4 mm) were hexagonally packed (comprising seven rods). The reason for choosing this form of packing was that: this form of packing provides the highest packing efficiency, and densest packing for straight cylinders when their axes are parallel [112], and also extends the interaction of energy between the rods [113] and geometrically all the pairs of neighbouring axes are located at a constant distance from each other. Also the non-bonded nature of different constituents in the wire, would result in significantly lower flexural and torsional rigidities as compared to a solid structure with similar cross-sectional area. The comparison of hybrid composite wires with several structures has been conducted in Chapter 4. Prior to the braiding process, only a single layer of tape was applied at both ends of packed rods and no form of adhesive was used to ensure integrity of the packing at this stage. The hybrid composite tensile armour wires with different configurations were manufactured with varying braid topology and braid angles, and two different types of rod diameters in the packing. The different configurations of hybrid wires produced and studied in this thesis have been shown in Figure

63 Study of Manufacturing Processes for Hybrid Wire Composite Wires For over-braiding the hexagonally packed rods, regular (2/2) and diamond (1/1) braid topologies were used, and three different braid angles (30, 45 and 55 ) were employed. The braid angle (or the bias angle) of a braid can be varied for any given core radius (R) by changing the take-up speed (v), or the rotational speed (ω) of the braiding machine, as depicted in Eq. (3.2). The Eq. (3.2), is valid for circular crosssections only obtained from [91], however it can be converted to suit the geometry of the hybrid wire cross-section in form of Eq. (3.3) (derived in Appendix; Page 176), which is valid for a hexagon cross-section with filleted edges, where r is the radius of individual rod used in the pack and the θ hcw is the braid angle for hybrid composite wire. θ = tan -1 ( Rω v ) (3.2) θ hcw = tan -1 rπ + 6r [( ) ( ω π v )] (3.3) HCW with Φ 4 mm rods and 2/2 braid HCW with Φ 4 mm rods and 1/1 braid HCW with Φ 2 mm rods and 1/1 braid Figure 3.4: Different configurations of hybrid composite tensile armour wires Note - HCW: Hybrid composite wires; θ is the braid angle. 62

64 Study of Manufacturing Processes for Hybrid Wire Composite Wires Hexagonal pack of Ф 2 mm rods Over-braiding with 12 carriers for diamond (1/1) braid by using a 24 carrier braid machine Hybrid wire with Ф 2 mm rods, braid angle of 45, 1/1 braid Hexagonal pack of Ф 4 mm rods Over-braiding with 24 carriers for regular (2/2) braid by using a 24 carrier braid machine Hybrid wire with Ф 4 mm rods, braid angle of 45, 2/2 braid Hexagonal pack of Ф 4 mm rods Over-braiding with 24 carriers for diamond (1/1) braid by using a 48 carrier braid machine Hybrid wire with Ф 4 mm rods, braid angle of 45, 1/1 braid Figure 3.5: Hybrid composite tensile armour wire manufacturing processes 63

65 Study of Manufacturing Processes for Hybrid Wire Composite Wires The interlacement of a braided structure, determines the topology of a braid, and depends on the number of bobbins involved in producing that braid. If a bobbin is removed from the carrier of the machine, the interlacement of that yarn or tow through that braid pattern also gets removed. As described in detail in Chapter 2, the most commonly used interlacements in braiding are diamond (1/1), regular (2/2), and Hercules (3/3) braid. The Hercules braid (3/3) cannot be produced on either of the two: 24 and 48 carrier braiding machines present in university facility. This is because in order to produce a Hercules braid, the horngears in the braiding machine would require 6 slots in the machine horngears, whereas the horngears in the two braiding machines present, had only 4 slots, not allowing the production of Hercules braid. In order to over-braid the hexagonal packed rods, to produce hybrid composite armour wires, the primary aims during braiding were: Obtain diamond (1/1), or regular (2/2) braid topology : The reason for selecting these topology, as stated above is that, these are most commonly braid topologies and yield a braid with regular pattern. Other patterns like 2/1 or 3/2 could be used but may require complex selection of carriers, which unlike diamond or regular, require easier selection of carriers on either of two braiding machine (using all carriers results in regular braid, and half the number, when alternate carrier is left empty, results in diamond braid) Achieve full braid coverage: The reason full braid coverage is that when these wires are wound into the riser to form tensile armours, the neighbouring wires interact only with the braid fibres (lower coefficient of friction of 0.055) and not with the composite rods (higher coefficient of friction of 0.49), to reduce frictional forces. The quantification of effect of coefficient of friction between the nonbonded components in hybrid composite wires has been discussed in detail, later in the thesis. Use minimum number of carriers: Using lesser number of carriers would imply less material usage. 64

66 Study of Manufacturing Processes for Hybrid Wire Composite Wires Over-braiding process: Pack with Ф 2 mm rods The over-braiding of the hexagonal pack of Φ 2 mm rods was first carried out by using a 24 carrier braiding machine. A diamond (1/1) braid topology was obtained (as shown in Figure 3.5 (a)) by employing only 12 carriers. The reason for using only 12 carriers was that, by using 24 carriers on both 24 and 48 carrier braiding machine, would only allow braiding of the packed rods at very low angles (< 22º), that too with a very tight grip, whereas the braiding of higher angles (> 22º) would lead to a denser braid, with braid diameter (without the core) being higher than the thicknesses of the pack (core) itself, resulting in no grip on the packed rods. Another reason for using 12 carriers is the reduction in number of carriers to be used, yet providing full coverage (beyond certain braid angle). The 12 carriers on 48 carrier braiding machine cannot be used as the resultant braid would have no interlacement, and will actually be a filament wound structure. Hence, the 24 carrier braiding machine was employed, in which only 12 carriers (leaving alternate carriers empty) were used. The Figure A. 1 (Pg. 175) in the appendix depicts the braiding of packed rods with Φ 2 mm rods with 24 carriers Over-braiding process: Pack with Ф 4 mm rods The hexagonal pack of Φ 4 mm rods were over-braided by using 24 and 48 carriers braiding machines. All 24 carriers on the 24 carrier machine were used to produce a regular (2/2) braid topology (as shown in Figure 3.5 (b)); and only 24 carriers on a 48 carrier machine were employed to obtain a diamond (1/1) braid topology (as shown in Figure 3.5 (b)). These two configurations were considered to study the effect of braid topology on the mechanical properties (i.e. flexural and torsional rigidities) of hybrid composite wires. The usage of all carriers on the 48 carrier braiding machine would yield braid diameter being higher than the thickness of the packed rods with Φ 4 mm rods. This would enable braiding only at very low braiding angles (< 19º) with very tight grip; however, at higher angles the braid diameter will exceed the thickness of the packed rods itself resulting in loose or no grip on the packed rods. Long lengths of rods were braided on both braiding machine to produce the hybrid composite wires which helped in: 65

67 Study of Manufacturing Processes for Hybrid Wire Composite Wires Faster production of test specimens, as braiding of each specimen separately would be time consuming, since the machine has to be reset for each of the specimen. The test specimens of each type of braid configuration were all cut from the same length of packed rods braided, to ensure uniformity, and reduction in the deviations within the same set of specimens during mechanical tests or other form of examination. Reverse braiding Braid jamming Figure 3.6: Reverse braiding and braid jamming phenomenon. In order to study and compare the flexural and torsional behaviour of the hybrid composite wires with the hexagonal pack of Φ 2 mm rods and of Φ 4 mm rods, the same range of braid angles (30, 45 and 55 ) had to be chosen, that resulted in almost 66

68 Study of Manufacturing Processes for Hybrid Wire Composite Wires full braid coverage with no avoid braid jamming or distortion. The braid jamming limits by the maximum and minimum braid angles possible without any shear distortion [88]. The lowest achievable braid angle, using 12 carriers on 24 carrier braiding machine was equal to 28 ± 1.2 that provided 98.5% braid coverage for the packing with Φ 2 mm, and the highest braid angle achievable, without any distortion or jamming of the braid, was 57 ± 1.5. The angles above 57 ± 1.5 resulted in jamming of the braid, accompanied by reverse braiding (shown in Figure 3.6). The maximum braid angle at the zero convergence length for packed rods with Φ 2 mm rods, was equal to 61 ± 0.8. For braiding packed rods with Φ 4 mm rods, wider range of braid angles could be braided, between 25 to 65, with almost full braid coverage and no braid jamming. However to ensure same braid angles were used for both types of packing, one with Φ 2 mm rods, and other with Φ 4 mm rods, same braid angles of 30, 45 and 55 were employed to study the effect of braid angle upon mechanical properties of hybrid composite armour wires. The bobbin carrier tension was maintained at 150 grams during braiding for all configurations of braided specimens produced. The carrier tension on both 24 and 48 carrier braiding machine, is set using spring tensioner system located in the bobbin carrier itself. The tension of 150 gram was chosen as it yielded uniform braid formation. Lower carrier tensions, result in overfeeding of the tow, that are slack (as observed in Figure 3.7) and do not yield uniform braid formation. Higher braid tensions, would yield uniform braid formation, however the range of angles (30, 45 and 55 ) chosen would reduce further, since high carrier tension causes the fibre tows to thicken, reducing the overall width of the tow being braided, resulting in reduction of the braid coverage. 67

69 Study of Manufacturing Processes for Hybrid Wire Composite Wires The tows become slacker as the carriers come closer to the braid ring, due to no significant tension contribution from bobbin carriers Figure 3.7: Braiding at low carrier tension of only 50 grams 3.3. Measurement process: Braid structural parameters This section includes the process of measurement of braid parameters that include: braid angle, braid thickness, width of tows in braid, and braid crimp Braid angle The braid angle has been measured using a digital protractor upon braiding of the rods at several points (50 points per metre) along the length of specimen and along the circumference (as much data points as possible). The method of measurement of the braid angle has been shown in Figure 3.8. The second form of measurement of braid angle was through image analysis, through Image J 1 software, where several images of braid along the length of the specimen and along the circumference taken were 1 Image J: A scientific image processing application that uses Java script (open source software) 68

70 Study of Manufacturing Processes for Hybrid Wire Composite Wires analysed; the full angle (double the value of braid angle) was measured as shown in Figure 3.8b, and the value was then halved to obtain the value of the braid angle. Measured value of 60.3 (a) Value of full angle (2θ) measured (b) Figure 3.8: Braid angle measurement through: (a) digital protractor and (b) image analysis.. 69

71 Study of Manufacturing Processes for Hybrid Wire Composite Wires The values obtained from physical measurement, and through image analysis were then averaged to get a final value for a braid angle for a specimen. The process was then repeated for 4 more specimens and the average value was taken as the value of the braid angle, obtained for set machine setting (machine and take-up speed), for pack with particular rod diameter Braid thickness The braid thickness has been measured using two different techniques: firstly by using perimeter method and secondly through the measurement of total thickness of hybrid composite wires. The first technique involved measurement of the perimeter of hybrid composite wires, using a rectangular strip of paper, wider at the one end containing a cavity in shape of a square. In order to measure the circumference using this strip, one end of the strip was passed through the other end of the strip through the square cavity created, and was pulled until the strip could not be pulled anymore. At this point a line was marked along the width of this pulled strip where it met the edge of the square cavity (shown in Figure 3.9b). The length between the marked line and the edge of the square cavity closer to the other end was measured with the help of Vernier calliper, to obtain precise measurement of perimeter of the hybrid composite wires. The measured perimeter of hybrid composite wire was then deducted from the perimeter of hybrid composite wires without braid (P pr ) obtained analytically using simple geometric equations, in order to obtain value of braid thickness. The perimeter of hybrid composite wires without braid (packed rods) was calculated using Eq. (3.4). The perimeter of hybrid composite wires (P pr ) is in the shape of a hexagon with filleted edges. P pr = 6 ( πr 3 ) + 6(2r) (3.4) In the second technique, thickness of hybrid composite wires (containing over-braid sleeve and the rod packing), was measured using Vernier calliper. The thickness T1 of the packed rods with Ф 2 mm rods was found to be 6.0 ± 0.01 mm and T2 equal to 70

72 Study of Manufacturing Processes for Hybrid Wire Composite Wires 5.53 ± 0.01 mm, measured using Vernier calliper. For Ф 4 mm packed rods the thickness T1 was found to be 12 ± 0.02 mm and thickness T2 was measured to be ± 0.02 mm. The thicknesses T1 and T2 were measured at 50 different points per metre of specimen length, and then the averaged to obtain representative thicknesses: T1 and T2. (a) (b) Figure 3.9: Process of braid thickeness measurement using: (a) circumference of the hybrid composite wires and (b) thickness of hybrid composite wires The thicknesses: T 1 and T 2 which are the thicknesses of hybrid composite wires, were also measured at 50 different points per metre of specimen along its length (shown in Figure 3.9b). The obtained values of both thicknesses, was then averaged to obtain final value the braid thickness of a specimen. The process was repeated for 4 more specimens, and then the average value (obtained from all 5 specimens) was taken as a representative of the braid thickness (t b ) of hybrid composite wires using Eqs. (3.5) & (3.6), with specific individual rod diameter, braid angle, and braid topology. Although theoretically there should be no difference between the thicknesses: T 1 and T 2, but physically a very small deviation (± 0.003) was found between the two. t b = T 1 T 1 2 (3.5) 71

73 Study of Manufacturing Processes for Hybrid Wire Composite Wires t b = T 2 T 2 2 (3.6) t b T1 T 1 T2 T 2 Figure 3.10: Schematic of cross-section of hybrid composite wire showing different thicknesses of components Tow width Value of measured length Figure 3.11: Process of measurement of tow width using image analysis software 72

74 Study of Manufacturing Processes for Hybrid Wire Composite Wires The tow width for over braid sleeve has been measured physically using Vernier calliper and through image analysis using ImageJ software (shown in Figure 3.11). Similar to the other braid parameters measurement, the tow width was measured at 50 points per metre specimen, and different points along the perimeter, for 5 specimens. The average of the value of the all the measurements obtained was then used as a representative for specific hybrid composite wire configuration Braid crimp The crimp phenomenon in a braid refers to the waviness or undulation of a tow as a result of interlacement between tows. Crimp for a braid can be quantified as the ratio of the difference between the length of the crimped tow (Lc) and the length of the noncrimped tow (Lnc) to that of the projected length (Lnc). The braid crimp percentage (C), for all the configurations of braided specimens was calculated using Eq. (3.7). The crimp factor (α) derived from crimp ratio (A), can be used to calculate the crimp angle (β) that the tows make upon crossing over and under other tows during braiding. The Eqs. (3.7) to (3.10) have been taken from ISO [114]. Lc > Lnc Hybrid composite wire Hybrid composite wire with a tow The length of the crimped tow (Lc) removed The length of the noncrimped tow Figure 3.12: Schematic representation of the crimp determination process 73

75 Study of Manufacturing Processes for Hybrid Wire Composite Wires C = (L c L nc )/(L nc ) 100 (3.7) A = L c /L nc (3.8) α = A 1 (3.9) β = tan 1 α (3.10) The length of the crimped tow (Lc) and the length of its projection inside the braid (Lnc), which is the key to determine the braid crimp and braid crimp angle, was measured for 5 specimens of each type of hybrid composite wires, and for each of the specimen, 5 tows with a long helical length of 5-10 cm to get as precise measurement as possible. The length of the non- crimped tow was measured for the same tow (when inside the braid), being investigated for braid crimp Results: Braid parameters The measured braid parameters have been shown in Table 3.1. If the values of braid angles are observed, there are deviations among them, although marginal. It is not possible to get a perfect braid angle, as when measured physically or through the analysis of different images taken, there will always be some deviation. If the values of braid thickness and tow widths are observed in Table 3.1, it can be seen that the braid thickness increased with increasing braid angle, while the tow width decreased with increasing braid angle for the hybrid wires of Φ 2 mm and Φ 4 mm rods, clearly showing their inter-dependence. If it is assumed that the perimeter of a tow in a braid remains same at any given braid angle (assuming the bobbins are perfectly wound, and the fibres in tow are not twisted), the braid thickness and the tow width are interdependent such that an increase in the tow thickness would lead to a decrease in the tow width and vice versa. 74

76 Study of Manufacturing Processes for Hybrid Wire Composite Wires In case of braid crimp, as it can be observed in Table 3.1, for hybrid composite wires with Ф 2 mm, when braid angle was increased from 30º to 45º, an increase of 56% was observed; a further increase of 35% in braid crimp was observed when the braid angle was increased from 45 to 55. Similar trend of an increase in braid crimp with an increase in braid angle was observed in case of hybrid composite wires with Ф 4 mm. As the braid angle was increased from 30º to 45º, the braid crimp increased by 12% for diamond braid and 36% for regular braid; as the braid angle was further increased from 45º to 55 º, the braid crimp increased by 79% for diamond braid and 52% for regular braid. This trend of increase in braid crimp with an increase in braid angle was due to the increase in braid density, which increases as more tows are deposited per unit length. The crimp value will be also be a minimum when the braid angle is closer to 0º, and maximum when the braid angle is closer to 90º [90]. The effect of braid topology on braid crimp was also found to be quite significant for in case of 30º and 55º braid angles where a decrease in braid crimp of 18% for 30º braid angle and a further decrease of 14% for 55º braid angle, was observed as the topology was changed from diamond to regular. However, in case 45º braid a smaller decrease in braid crimp of only about 0.8% was observed as the topology was changed from diamond to regular. When diamond and regular braids are produced using same number tows, same length of tow in a regular braid will experience lower crimp as compared to diamond braid due the its higher float length, which has also been observed in case of hybrid wires Theoretical and experimental braid cover factor The theoretical coverage value by the braided yarns or tows on the surface they are braided on (either core or a mandrel), has been quantified in terms of cover factor (C f ), which has been quantified in form of Eq. (3.11) in [91] using: width of the yarn or tow (w), number of carrier employed during braiding (Nc), radius of the circular (crosssection) mandrel/core (R) and braid angle (θ). 75

77 Study of Manufacturing Processes for Hybrid Wire Composite Wires C f = 1 - ( 1 C fhw = 1 - [1 2 W y N c 4πRcosθ ) (3.11) 2 wn c 4r(π + 6) cosθ ] (3.12) Figure 3.13: Theoretical and experimental cover factor for hybrid armour wires with Ф 4 mm rods, using 12 carriers on a 24 carrier braiding machine (containing the images of the hybrid wires) 76

78 Study of Manufacturing Processes for Hybrid Wire Composite Wires Table 3.1: Structural properties of braids Type Braid topology Braid angle Crimp Angle Braid thickness Tow width Braid crimp Crimp ratio (⁰) (⁰) (mm) (mm) (%) 1 1/1 30 ± ± ± ± ± ± /1 45 ± ± ± ± ± ± /1 55 ± ± ± ± ± ± /1 30 ± ± ± ± ± ± /1 45 ± ± ± ± ± ± /1 55 ± ± ± ± ± ± /2 30 ± ± ± ± ± ± /2 45 ± ± ± ± ± ± /2 55 ± ± ± ± ± ±

79 Study of Manufacturing Processes for Hybrid Wire Composite Wires The Eq. (3.11) has been modified in form of Eq. (3.12) (derived in Appendix, Page 177), to suit the cross-section geometry of hybrid wires (i.e. hexagon with filleted edges). The cover factor of over-braid sleeve in hybrid wires (C fhw ) can be quantified using the width of the tow (w), number of carriers (Nc), braid angle (θ), and individual rod diameter (r). The equation has been validated using different configuration of hybrid composite wires, which are hybrid wires with Ф 4 mm rods, diamond braid topology, at three braid angles: 30, 45, and 55. These configurations gave a broad range of braid cover factor (shown in Figure 3.13) unlike the configurations studied in this thesis that majorly have same braid cover factor of nearly 1 (braid coverage nearly 100%). The broad range of cover factor also helped in determining the effect of braid angle on the braid cover factor. As observed in the in Figure 3.13, the theoretical cover factor is in very good agreement with experimental cover factor, with maximum deviation of ± 0.02 for 30 braid angle. The effect of braid angle is also evident in Figure 3.13, where an increase in braid angle led to an increase in braid coverage both theoretically and experimentally, such that as the braid angle was increased from 30 to 45 experimentally, the braid cover factor increased by 22.8% and as the braid angle was further increased from 45 to 55, the braid coverage increased by 11.6%. The effect of employing number of bobbin carriers was also found to be highly significant if both Figure 3.4 (for hybrid wires with Ф 4 mm rods, and diamond braid topology) & Figure 3.13 are compared, where an increase of nearly 27% for 30 braid angle, increase of nearly 13% for 45, and a smaller increase of 3% for 55 braid angle was observed Quantification of the tow tension during the braiding process The tension in the tows during braiding process is dependent upon several parameters that include: the braid angle, coefficient of friction between the fibre tows and every surface it makes contact with, and the angle it subtends with every point of contact. A 2-D schematic has been drawn to explain the braiding process and the tension in the fibre tows due to braiding process, with help of only two carriers, in Figure

80 Study of Manufacturing Processes for Hybrid Wire Composite Wires Bobbin Tension T2 Take-up direction Braid tows Tension T3 θ Guide ring Tension T1 Deck Braid fell position Tows being fed for braiding Figure 3.14: 2-D Schematic representation of tension mechanism during braiding process using just two carriers The motion of the bobbin carriers that feed the fibre tows for braiding is not circular one, but in form of a serpentine motion (a closed sine or cosine wave). Due to this serpentine motion, the angle (referred to as θ ) that the fibre tows (fed out of the guide eyelets of the bobbin carrier) make with the braid ring (horizontal plane tangential to braid ring) will vary harmonically with a maximum and a minimum value, which would result in infinite number of θ values between maximum and minimum angle values. An interlacement pattern is formed between as the bobbin carrier move from maximum to minimum angle: θ or vice versa. Ideally, the tension in the tows will be an aggregate of tensions at every angle (θ ), on the closed sine wave, which is not possible to deduce. Hence, only maximum and minimum angle values of θ, have been used to quantify the aggregate tension in the tows in form of tension T3, which also is an approximate value of tension at which the tows are being interlaced to form braid. The tensions experienced by the fibre tows during braiding, can be divided into three zones: the first zone lying between the carrier guide eyelet and the pulley of the bobbin carrier (both components shown in Figure 3.15a), the second zone lying between the 79

81 Study of Manufacturing Processes for Hybrid Wire Composite Wires braid ring and the carrier guide eyelet, and the third zone lying between the braid fell position (point at which braid starts to form) and the length of the fibre tow extending up to the guide ring. The tow tension T0 shown in Figure 3.15a, was measured to be equal to 1.5 ± N, using digital tension measuring device. In order to quantify tow tension T3, the value of T0, was converted to tension T1, shown in Figure 3.14b, using Eq. (3.13), where θ is the angle the fibre tow make between the carrier pulley and imaginary horizontal axis tangential to guide eyelet of bobbin carrier. Due to the multiple contact points, fibre tows make with parts of braiding machine, the tension in the fibre tows during the braiding process can be quantified using Eqs. (3.13) to (3.15), where the Eqs. (3.14) & (3.15), can used depending upon whether the tow comes in contact with the braid ring during the braiding process. Several cases of tension that the fibre tows may encounter during braiding process have been shown in Figure 3.15 (b d). a) Case 1 The tension T0 of the tow without being in contact with the guide eyelet was measured to be 1.5 ± N. T0 Carrier guide eyelet Pulley of the bobbin carrier b) Case 2 The angle between fibre tow and braid ring θ is smaller than the braid angle θ. θ T3 T2 θ π - θ θ = 5.5 π -θ T1 80

82 Study of Manufacturing Processes for Hybrid Wire Composite Wires c) Case 3 The angle between fibre tow and braid ring θ is greater than the braid angle θ. This is a hypothetical case and is practically not feasible. T3 θ T2 θ π - θ θ = 5.5 π -θ T1 d) Case 4 This is a more likely case when the angle between fibre tow and braid ring θ is greater than the braid angle θ. This case implies no contact between the fibre tow and the braid ring. θ π - θ θ = 5.5 T1 T3 Figure 3.15: Schematic representation of different cases of tow tension that may be encountered during the braiding process T 1 = T 0 cos θ (3.13) T 3 = [T 1 e μ s[(π θ )+θ ] ]e μ s[(π θ)+θ ] (3.14) T 3 = T 1 e μ s[(π θ)+θ ] (3.15) The possibility of whether the fibre tows will come in contact with the braid ring will entirely be dependent upon the braid angle. If the braid angle (θ) is greater than angle θ, that the fibre tows make the braid ring (as shown in Figure 3.15b), there will be contact between the fibre tows and braid ring. However, as the braid angle becomes less than θ, there will be no contact between the fibre tows and the braid ring (shown in Figure 3.15d). In case where there is no contact between the fibre tow and the guide ring, the Eq. (3.15) can be used, however if there is contact between the fibre tow and the guide ring, the Eqs. (3.14) can be used. 81

83 Study of Manufacturing Processes for Hybrid Wire Composite Wires If the distance between the guide ring and the plane containing the carrier is increased, the maximum and minimum braid angles will reduce, reducing the possibility of Case 4 (shown in Figure 3.15d). The presence of guide ring although increases the tension in the tow by adding another contact point, it is essential for braiding for: Reverse braiding: if more than one layer of braid is required, reverse braiding can be used for continuous production of multiple braid layers. Provides additional guides to be mounted onto the braid ring helping in guiding the core for take-up process, helping in better and more efficient braiding process. The braid ring helped in guiding of the bundle of rods, holding the non-bonded rods together, and helping in stable braid formation. T0 γ T 0 T0 Stainless steel rod (a) (b) Figure 3.16: Schematic representation of methodology used for calculating coefficient of friction using braid carriers The aggregate tow tensions at each of the braid angle, with respective braid topology, and machine type (24 or 48 carrier braiding machine used) have been calculated and reported in Table 3.2. The coefficient of friction between the Dyneema fibres and the braid ring that constitutes of stainless steel was calculated using capstan s equation [115] represented by Eq. (3.16) and Figure 3.16, as ± The coefficient of friction between the Dyneema fibres and guide eyelet of the bobbin carrier that constituted of brass was also found to be similar to the coefficient of friction between the fibres and braid ring (stainless steel). The process of measurement of coefficient using this method proving to be a straight forward and simpler way of calculating static coefficient of friction between fibres and different solids surfaces. 82

84 Study of Manufacturing Processes for Hybrid Wire Composite Wires μ s = lnt 0 γlnt 0 (3.16) Type Table 3.2: Tow tensions for different braid configuration (T0 = 1.5 N) Machine used (number of carriers) Braid angle (⁰) Individual Rod diameter (mm) Topology Tension (T3) (N) / ± / ± / ± / ± / ± / ± / ± / ± / ± 0.33 As observed in Table 3.2, the tension in the tows differs for each braid angle. The tension decreased as the braid angle was increased (although marginally). The reason for this trend is that as the braid angle increases, the convergence length associated with that braid angle also increases, increasing the length of the tow between the braid fell position, and the guide eyelet of the bobbin carrier. This increase in length of tow induces more tension in the tows being braided. Conversely, as the braid angle decreases, the associated convergence length and the length of tow between the braid fell position and guide eyelet of the bobbin carrier also decreases, inducing lesser tension as compared to lower braid angles. The high deviation in the tow tension is due to the variation of angle θ, that varies harmonically with a maximum and minimum value. Although the tow tension values in Table 3.2 vary marginally, still the theoretical predictions can be useful when using fibres that have very high coefficient of friction values, where the values of tension between different braid angles may vary significantly. 83

85 Study of Manufacturing Processes for Hybrid Wire Composite Wires 3.4. Summary The process of manufacturing hybrid composite wires for tensile armours was described in this chapter. Both braiding and pultrusion processes can help in continuous production of long lengths of hybrid composite wires. However, the quality of composite rods has to be examined (presence of misaligned fibres, damaged fibres, twisted fibres, and voids) before braiding, in order to achieve higher tensile stiffness and strength due to unidirectional nature of fibres in these rods. The effect of varying the braid angle and braid topology on the structural parameters (braid tow width, braid thickness and braid crimp) of braid sleeve was found to be significant. A theoretical equation for braid cover factor was presented using analytical equation present in literature, which could be very useful. The equation helps in predicting a close agreement with the experimentally obtained braid cover factor values. A detailed analysis of tension experienced by the tow during the braiding process has been conducted and an analytical solution to quantify the tension of the interlaced tow inside the braid has been presented. The quantified solutions of the tension experienced by the tows during braid process in different scenarios (tow with or without contact with the braid ring), can be highly useful to quantify the constant hoop pressure exerted by the braid tows on the packed rods that has been discussed in detail in following chapters. 84

86 Mechanical Testing and Characterisation of Hybrid Composite Wires Mechanical Testing and Characterisation of Hybrid Composite Wires T his chapter describes the methodology used for mechanical testing of the hybrid composite wires, accompanied by a detailed analysis of the results. The flexural and torsional mechanical tests have been used to characterise the mechanical performance of hybrid composite wires. The mechanical performance of the hybrid composite wires has been compared with metallic structures with similar dimension (cross-sectional geometry) as these wires, and with traditional armour wires Mechanical tests procedures The mechanical tests (flexure and torsion) conducted for all configurations of hybrid armour wires, helped to determine the effect of braid angle, braid topology, and individual rod diameter upon the mechanical performance of these wires. Tensile and shear tests for single composite rods with Φ 2 mm and Φ 4 mm, were also conducted in order to determine their axial (E11) and shear (G12) modulus. The tensile tests for hybrid composite wires have not been conducted, since the axial modulus of the hybrid composite wires, that contain hexagonal packed non-bonded rods, will be same or close to the axial modulus of individual composite rods (there will be negligible contribution from over-braid sleeve) Flexure tests There are no specific testing standards available for testing a structure or a material system similar to the hybrid composite armour wires, hence from the available flexural test standards (ASTM [ ], ISO [119], and BIS [120]), the most suitable available standard for fibre reinforced composite materials: ASTM D7264 [118] was chosen. The ASTM D7264 [118], consists of flexural test procedures for both three point and four point type of flexural tests. Both three and four point flexural tests were chosen, as the hybrid wires are a combination of multiple non-bonded structures, and 85

87 Mechanical Testing and Characterisation of Hybrid Composite Wires a non-homogenous material, by using both types of flexural tests, the flexural properties could be rectified. However, only four point flexural test was incorporated for testing the specimens till the maximum possible mid-span deflection of 55 mm, whereas for the three point flexural test, the specimens have been tested only till 22.5 mm mid-span deflection. The reason for choosing four point flexural test, for testing specimen till the maximum deflection possible, is due to the bending moment and flexural stress, that remains constant between the two inner point loads and most importantly it gives a better representation of the flexural behaviour of hybrid wire bent around the pipe [108]. Two types of edge boundary conditions were used to determine the flexural properties of hybrid composite armour wires and the individual rods used in their packing, using four point flexural test. The first type of edge boundary condition involved the ends of the specimen to be taped within 10 mm at both ends using the high performance tape, mimicking flexural behaviour of long lengths of armour wires. However, in the second edge boundary condition the ends of the specimens were bonded together, by the application of a structural adhesive, within 10 mm at both ends, depicting the flexural behaviour of armour wires near the end fittings of the flexible riser. The first type of boundary condition was investigated for all configurations of hybrid wires. The second type of edge boundary condition was investigated only for one braid configuration of hybrid armour wires: with Φ 4 mm rods, and regular braid topology. For the four point flexural test, 5 specimens each of all configurations of specimens have been tested, with chosen span to thickness ratio of 32:1, where the span length of 176 mm was used for packing with Φ 2 mm rods, and a span length of 352 mm was chosen for packing with Φ 4 mm rods. Same span length has been chosen for hybrid wires with same diameter rods, as it helped in better capturing the effect of changing braid parameters (braid angle and braid topology). For flexural testing of the single rods, there already exists a standard [121], to test circular pultruded rods however, it can only be applied for the three-point type of flexural test and also requires a different type of test fixture. Therefore, the same test 86

88 Mechanical Testing and Characterisation of Hybrid Composite Wires standard of ASTM D7264 [118] has been followed for flexural testing of single rods. For Φ 2 mm rod, the span length of 64 mm was used and the Φ 4 mm rod, span length of 128 mm was used. The flexural behaviour of single rods was also investigated at the same span length as the hybrid composite wires they are used in, and tested only upto 10 mm mid-span deflection; the results have been reported in Chapter 5, for computational modelling. The hybrid armour wires with Φ 4 mm rods could only be tested to the maximum of ~ 2% flexural strains (55 mm mid-span deflection) due to the limitations of the test rig. However, hybrid wires containing Φ 2 mm rods, were tested up to ~ 4% flexural strains (55 mm mid-span deflection) depicted in Figure 4.1. The results for wires with Φ 2 mm rods, have only been reported till 2% strains to compare with hybrid wires containing Φ 4 mm rods. The 2% strain for hybrid composite wires with Φ 2 mm rods, corresponds to curvature of 7 m -1, whilst for Φ 4 mm rods, it corresponds to curvature of 3.5 m -1. For three point flexural tests that were incorporated to rectify the flexural (elastic) properties obtained using a four point flexural test, same flexural testing standard was incorporated (as mentioned above), with the same span to thickness ratio of 32:1. Only 3 specimens were tested for each type of braid configuration. The flexural strain (εf) was calculated using Eq. (4.2), defined in ASTM D7264 [118] as the maximum strain at the surface of a specimen occurring at mid-span, which can be calculated with the help of mid-point deflection (δmax) measured using a video extensometer, specimen thickness (h) and the span length (L). The cross-head speed of 5 mm/min as recommended in the standard was used with the maximum capacity of a load cell of 10kN. EI = M/κ (4.1) ε f 3PT = 6δmax h / L2 (4.2) ε f 4PT = 4.36δmax h / L2 (4.3) 87

89 Mechanical Testing and Characterisation of Hybrid Composite Wires κ = 2ε f / h (4.4) δmax = 0 mm δmax = mm δmax = 22.5 mm (a) δmax = 0 mm δmax = 22.5 mm δmax = 55 mm (b) δmax = 0 mm δmax = mm δmax = 22.5 mm (c) δmax = 0 mm δmax = 22.5 mm δmax = 55 mm (d) Figure 4.1: Flexural tests being conducted on hybrid composite wire using: (a) three point flexural test (for hybrid wires with Φ 2 mm rods), (b) four point flexural test (for hybrid wires with Φ 2 mm rods), (c) three point flexural test (for hybrid wires with Φ 4 mm rods), and (d) four point flexural test (for hybrid wires with Φ 4 mm rods) 88

90 Mechanical Testing and Characterisation of Hybrid Composite Wires The flexural rigidity of an isotropic structure can be quantified by the product of tensile modulus (E), and area moment of inertia (I). As the hybrid composite wire is not isotropic material, the flexural rigidity for all configurations of tested specimen was calculated experimentally using the slope of the flexural moment (M) versus curvature (κ), shown in Eq. (4.2), between µε as per ASTM D7264 [118]. The flexural strains for three point (ε f 3PT ) and four point (ε ) can be quantified using f4pt Eq. (4.2) and Eq. (4.3). The curvature of a structure subjected to flexural loads can be calculated from specimen thickness (h), and flexural strain (ε f ) as defined in Eq. (4.4) Torsion tests The torsion tests (as shown in Figure 4.2) were carried out for hybrid composite wires, with Φ 2 mm rods and Φ 4 mm rods, till the maximum limit of 400 /m (40 twist angle), due to the machine limitation. 5 specimen of each type of hybrid wire configuration were tested, using a gauge length of 100 mm. As the twist is applied on one end of hybrid composite wire, the exterior rods in the hexagonal packed structure wrap around the centre rod that result in generating complex strain components for both the braid and the rods surrounding the central rod. As, the aim of the test was primarily to determine the shear properties of the hybrid composite wires as whole, angle of twist was obtained from the load cell rotation itself, by assuming the structure of hybrid wire, as a homogenous material. Since, the application of the strain gauges onto the braid would damage the braid and distort the braid angle; the strain gauges could not be applied on to the rods, due to their high curvature. There are no available standards to test a structure similar to hybrid composite wire, that has a cross-section similar to a hexagon with filleted edges, and comprising multiple non-bonded materials. Therefore, two approaches were incorporated to determine the most effective technique to hold the ends of the hybrid composite wire together (in the clamped region) whilst under twist. In the first technique, the ends of the hybrid composite wires were coated within 20 mm using Araldite epoxy based resin-hardener mixture, and then inserted in a 20 mm long cylindrical aluminium pot used as tabs, which also contained the same resin and hardener mixture. It was 89

91 Mechanical Testing and Characterisation of Hybrid Composite Wires however made sure, that each end was tabbed one at a time by keeping the specimen vertical (tabs on surface), since tabbing two ends simultaneously would involve keeping the specimen horizontal, resulting in non-uniform spreading of resin-hardener mixture. Also, by keeping the specimen vertical, the resin-hardener mixture did not seep into the gauge length. Only once the resin-hardener mixture cured, the other end was tabbed using similar procedure. In the second technique, the aluminium pots were not incorporated. However, the rods and the braid were bonded together within 20 mm of both ends using the same resinhardener mixture, as used in the first approach. Just like the first approach, the resinhardener mixture was applied at keeping the specimen vertical, and only at lower end, to avoid the resin-hardener to seep through the gauge length. In order to grip the hybrid wires, V grips were used, which helped in ensuring that no slippage occured between the clamps and the wire ends, during the application of twist. Circular grips could not be used due to the cross-sectional shape of the hybrid composite wires (resulting in empty spaces), due to which the grips were not able to twist the structure effectively, especially the central rod. Although the use of V-grips resulted in minor compression along the thickness of ends of specimen till about 5 mm at both ends, the compressed portion, helped in effective twisting of the entire structure. The compressed portion also lied within the grips, and was not part of the gauge length, where no effects of small compressed thickness along the specimen ends were observed. The lowest possible cross-head rotation speed of 1 /min was used for all configurations of tested specimen, to provide greater accuracy of the results. From the test results obtained from the two approaches mentioned above, the first approach resulted in very high deviations within the same type of specimens tested, due to the aluminium tabs that got crushed under the grip leading to slippage and entanglement with the braid during the test. The second technique, due to absence of aluminium tabs, resulted in significantly lower deviation among the same type of specimens tested. Therefore, the second type of technique was incorporated to test the remaining specimens. The load cell used in torsion tests had a maximum torque capacity of 1000 Nm, which was nearly 1500 times higher than the maximum torque observed for 90

92 Mechanical Testing and Characterisation of Hybrid Composite Wires hybrid composite wires with Ф 2 mm rods, and 125 times higher than the maximum torque observed for Ф 4 mm rods, resulting in high level noise in the generated data curves. Since, the noise for each specimen was consistent, linear and non-linear fitting of the curves was carried out using Origin software [122]. Due to the high level of noise generated (limitation of load cell), the single rods with Φ 2 mm and Φ 4 mm, were also tested under torsion to 400 /m twist per length, by closely following ASTM D3916 [123], but with a lower gauge length of 50 mm (lower noise), to compare the shear behaviour of a single rod with different configurations of hybrid wires. The twist angle for single rods was also determined using cross-head rotation as the application of strain gauge was not feasible due to very high curvature of the rods (a) (b) Figure 4.2: Torsion test to maximum limit of 40 twist angle for: (a) hybrid wire (45 braid angle) with Ф 2 mm rods and (b) hybrid wire (45 braid angle) with Ф 4 mm rods GJ p = T/(θ/L) (4.5) Torsional rigidity for an isotopic structure can be quantified by the product of its shear modulus (G) and its polar moment of inertia (J p ). However, as the hybrid wire is not an isotropic material, the torsional rigidity for all configurations of specimen tested were calculated experimentally, using the slope of torque (T) versus twist per length (θ/l) curve, as depicted in Eq. (4.5), obtained from [124]. The shear behaviour for all configurations of specimen tested is depicted in Figure 4.8. The torsional rigidity for 91

93 Mechanical Testing and Characterisation of Hybrid Composite Wires all configurations of tested specimen was determined from the slope of torque and twist per length, between µε conforming to both ranges specified in ASTM D3518 [125] ( µε) and ASTM D5448 [126] ( µε), for fibre reinforced composite materials. The cross-sectional geometry of hybrid composite wires has been assumed to be circular for determining the shear strains for easier calculation of elastic range (twist per length) to be used for calculating the torsional rigidity Tensile tests for single rods The axial (E11) modulus of pultruded rods with Φ 2 mm and 4 mm, were experimentally determined by closely following ASTM D3916 [123]; however, the tensile modulus of UHMW-PE fibres (tow) was obtained from the manufacturer s technical data sheet. Five specimens of each rod diameter were tested. The tensile tests for hybrid composite wires as stated previously, have not been conducted, as the axial modulus of the hybrid composite wires, which comprises of hexagonal packed nonbonded rods, will be same or close to the axial modulus of individual composite rods (there will be negligible contribution from over-braid sleeve) Mechanical characterisation Axial and in-plane shear modulus of single rods The axial (E11) and in-plane shear (G12) properties of pultruded rods with Φ 2 mm and Ф 4 mm have been reported in Table 4.1. The theoretical value of E11 and G12 for composite rods has also been computed, using rule of mixtures equation (Eq. (4.6)), and Halpin & Tsai equations (Eq. (4.7)) [127]. The Eq. (4.6) that uses micromechanical properties of composites in form of axial modulus of fibre (Ef), tensile modulus of matrix (Em) and fibre volume fraction (Vf). Whereas, in Eq. (4.7), the in-plane shear modulus of composite has been determined using shear modulus of fibre (Gf), matrix shear modulus (Gm), fibre volume fraction Vf, and parameter ξ = 1. E 11 = V f E f + V m (1 V f ) (4.6) 92

94 Mechanical Testing and Characterisation of Hybrid Composite Wires G 12 = G m(1 + ξηv f ) (1 ηv f ) (4.7) η = G f G m 1 G f G m + ξ Table 4.1: Material properties determined experimentally (for composite rods), and from manufacturer s technical data sheet and literature (for braid fibres) Material E11 G12 (GPa) (GPa) Composite rods (Ф 2 mm) 112 ± ± 0.5 Composite rods (Ф 4 mm) ± ± 0.1 UHMW-PE fibres 210 [128] 0.95 [129] The value of the theoretical axial modulus obtained using Eq. (4.6) was found to be 25% higher than the axial modulus obtained from experiments, for both diameter rods, while in case of in-plane shear modulus an increase of nearly 33% was observed if the theoretical values are compared with experimental values. The reason for this trend stems from the defects found in composite rods using microscopic analysis conducted in Chapter 3 (Pg. 59), in form of high void content, deformed fibres found along the cross-section of the composite rods (Figure 3.2); and miss-aligned fibres (see Figure 3.3) observed for both rod diameters. Whilst the tensile, shear, compressive and flexural strengths have been proven to decrease with increasing in void content [130], the presence of voids is not expected to decrease the axial or shear modulus of composite rods significantly. The reason for the lower axial and shear modulus is clearly due to the deformed fibres and miss-aligned fibres along the lengths of composite rods, which are capable of reducing the axial modulus and shear of the composite rods, significantly. 93

95 Mechanical Testing and Characterisation of Hybrid Composite Wires Flexural behaviour The flexural rigidity values of hybrid wires, and the individual rods used in their packing has been reported in Table 4.2. If the flexural rigidity of a single rod is compared with the hybrid composite wire they are used in, the flexural rigidity of hybrid composite wires with Φ 2 mm rods and wires with Φ 4 mm rods was found to be between 7-9 times the rigidity of the single rod used in its packing. The higher flexural rigidity for hybrid wire was due to the higher second area moment of inertia using Eq. (4.1). The effect of an individual diameter rod used in the pack of hybrid composite wires, was also seen to be highly significant, where for all three braid angles (30, 45, and 55 ), the flexural rigidity of hybrid wires with Φ 4 mm rods was found to be ~ 16 times the flexural rigidity of hybrid wires containing Φ 2 mm rods, due to an increase in second area moment of inertia. Specimen Type Table 4.2 : Flexural rigidities for all tested specimen EI4PT EI3PT (Nm 2 ) (Nm 2 ) Single rod Φ 2 mm 0.07 ± ± 0.01 Single rod - Φ 4 mm 0.95 ± ± 0.15 Diamond Φ 2 mm - 30º 0.53 ± ± 0.01 Diamond Φ 2 mm - 45º 0.54 ± ± 0.01 Diamond Φ 2 mm - 55º 0.55 ± ± 0.01 Diamond Φ 4 mm - 30º 8.85 ± ± 0.03 Diamond Φ 4 mm - 45º 8.64 ± ± 0.06 Diamond Φ 4 mm - 55º 8.89 ± ± 0.32 Regular Φ 4 mm - 30º 8.58 ± ± 0.02 Regular Φ 4 mm - 45º 8.81 ± ± 0.21 Regular Φ 4 mm - 55º 8.77 ± ± 0.33 The effect of braid angle on the flexural rigidity was found to be considerable but inconclusive. The minor change in the flexural rigidity due to the change in braid angle, experimentally (which remained inconclusive) could be due to the dry nature 94

96 Mechanical Testing and Characterisation of Hybrid Composite Wires of the braid. If the braid is impregnated with resin, its effect becomes more pronounced, and an increase in the braid angle can lead to a decrease in its flexural rigidity as observed in [105]. The flexural rigidity of the hybrid composite wires with diamond braid structure is expected to be lower due to a higher crimp value (reported in Table 3.1) as compared to regular braid topology, resulting in lower tenacity of the tows. δmax = 0 mm δmax = 22.5 mm (a) δmax = 55 mm Braid dislocation at point loads δmax = 0 mm δmax = 22.5 mm δmax = 55 mm (b) Figure 4.3: Four point flexural test on hybrid composite wires (with Ф 4 mm rods and regular braid topology) for: (a) 30 and (b) 45 braid angle The flexural behaviour of hybrid composite wires with Ф 2 mm rods can be observed in Figure 4.5, where none of the specimens braided, underwent any form of failure. The effect of the braid angle on the flexural rigidity of the hybrid composite wires was found to be insignificant up to 4.5 m -1 (~ 0.22 m radius of curvature) where the hybrid composite wires, all three braid angles of 30, 45, and 55 showed similar flexural rigidities (shown in Table 4.2). However, beyond ~ 4.5 m -1 curvature value, all the three braid angles showed non-linear behaviour. Similar flexural behaviour was also observed case of hybrid composite wires with Ф 4 mm rods, with both regular and diamond braid topologies. Similar elastic behaviour (flexural rigidity) was observed up to approx m -1 curvature (~ 0.44 m radius of curvature). However, beyond the 95

97 Mechanical Testing and Characterisation of Hybrid Composite Wires curvature of 2.25 m -1 all the three braid angles of 30, 45, and 55 wires showed nonlinearity. Matrix rupture due to compressive stresses Fibre splitting due to tension Fracture at point loads Minor Fibre Splitting due to tensile forces (a) (b) (c) Figure 4.4: Failed single rods during flexural test for (a) Ф 2 mm rod, (b) 4 mm diameter rod, (c) micrograph of the cross-section of fractured Ф 4 mm rod, at the point loads The non-linear behaviour for both types of hybrid composite wires with Ф 2 mm rods, and Ф 4 mm rods was observed to be most pronounced for the 30 braid angle (as shown in Figure 4.5) for wires with Ф 4 mm rods that underwent packing deformation, reducing the effective flexural rigidity of the structure, due to the reduction in the resultant second area moment of inertia and. No pack deformation was observed in case of higher braid angles of 45 and 55, but still the non-linear response was also observed, which was due to the combined effect of material and geometric nonlinearity. The non-linear behaviour could have also arisen due to the inter-rod interaction inside the packing, especially during high flexural deflections. If the maximum highest bending moment values are observed in Figure 4.5, the 55 braid angle showed the highest value, followed by the 45 and 30 braid angles among all hybrid wire configurations studied. The reason for 55 angle depicting highest 96

98 Mechanical Testing and Characterisation of Hybrid Composite Wires maximum bending moment values and no pack deformation, was due to being the densest braid, it has the strongest grip on the hexagonally packed rods. The flexural behaviour of single rods is presented in Figure 4.4, where both single rods with Ф 2 mm and Ф 4 mm experienced failure. The single rod with Ф 2 mm showed greater fibre splitting in the region between the load pins due to tensile (bottom face of rod) and compressive forces (upper face of the rod). The rod with Ф 4 mm showed fracture with permanent deformation at the point of contact with the load pins, due to the action of compressive forces on the surface. However, no major fibre splitting between the load pins was observed; this was more pronounced for rod with Ф 2 mm Effect of point load As mentioned in the methodology of the flexural testing, an additional three point flexural test as carried out for all configuration of tested specimen and single rods, to help determine the effect of point loads. The flexural rigidity for the four point and three point flexural tests were calculated from the slope of the bending moment versus curvature, between 1500 to 3000 µε as per ASTM 7264 [118]. The effect of the braid angle and braid topology on the flexural rigidity of tested specimens remained inconclusive and insignificant, as can be seen in Table 4.2. The maximum deviation between the flexural rigidity values obtained from the three point and four point flexural tests, was observed merely ± 0.35 Nm 2. The small change in flexural rigidity is an indicator that the flexural rigidity of the hybrid composite wires remains largely unchanged. 97

99 Mechanical Testing and Characterisation of Hybrid Composite Wires Non-linear response of 30 braid angle due to pack deformation, reducing the effective rigidity 55 braid angle depicting highest bending moment value due to strongest grip on the packed rods Non-linear response of 30 braid angle due to pack deformation, reducing the effective rigidity (a) (b) Figure 4.5: Flexural behaviour of hybrid wires and individual rods for: (a) Ф 2 mm rods and (b) Ф 4 mm rods 98

100 Mechanical Testing and Characterisation of Hybrid Composite Wires Effect of boundary conditions Two types of boundary conditions as stated in the methodology for flexural testing were examined, one with taped edges and one with bonded edges for both hybrid wires and packed rods without braid, (mentioned as braid absent in shown in Figure 4.7). Their flexural behaviour has been depicted using flexural load versus cross-head displacement curves, as the packed rods with no braid and taped edges, started to deform within 2 ± 0.5 mm of cross-head displacement, resulting in video extensometer not being able to record mid-span deflections. Debonding Rod slippage resulting in pack deformation Figure 4.6: Effect of edge boundary conditions 99

101 Mechanical Testing and Characterisation of Hybrid Composite Wires (a) (b) (c) (d) Figure 4.7: Effect of boundary condition for hybrid wire with Ф 4 mm rods: (a) without braid (taped edges), (b) without braid (bonded edges), (c) with braid (45, 2/2, taped edges), and (d) with braid (45, 2/2, non-bonded edges) The packed rods no braid and bonded edges, depicted similar behaviour as compared to specimens with taped edges, undergoing pack deformation, post bond failure, which occurred within 8 ± 1 mm of cross-head displacement. In case of hybrid wires (2/2, 45 ), the bond failure occurred at 8 ± 0.8 mm cross-head displacement between the rods, and a second bond failure occurred at 11 ± 0.5 mm, between braided fibres and rods. The flexural rigidity (using curvature from cross-head displacement) of bonded edged specimen was found to be almost twice that of the specimens with taped edges, for both hybrid wires and packed rods with no braid. Unlike the packed rods with no braid, no packing deformation was observed for either of bonded and taped edged hybrid wires. This finding helps to infer that the flexural rigidity of hybrid composite wires at the riser s end fittings will be twice that of flexural rigidity of these wires away from the end fittings. 100

102 Mechanical Testing and Characterisation of Hybrid Composite Wires Torsional behaviour The torsional rigidity of all configurations of hybrid armour wires manufactured, have been presented in the Table 4.3. If the torsional rigidity of Ф 2 mm single rod is compared with the torsional rigidity of hybrid composite wires with Ф 2 mm rods, an increase of nearly 8-16 times (depending upon braid angle) is observed. In case of hybrid composite wires with Ф 4 mm rods, their torsional rigidity was found to be times (depending upon the braid angle) the single rod used in their pack. Table 4.3 : Torsional rigidities for all tested specimen Specimen Type GJp (x 10-4 ) (Nm 2 deg -1 ) Single rod Φ 2 mm 0.84 ± 0.08 Single rod - Φ 4 mm 6.14 ± 1.62 Diamond Φ 2 mm - 30º ± 0.26 Diamond Φ 2 mm - 45º ± 1.06 Diamond Φ 2 mm - 55º ± 0.11 Diamond Φ 4 mm - 30º ± Diamond Φ 4 mm - 45º ± 7.14 Diamond Φ 4 mm - 55º ± 7.92 Regular Φ 4 mm - 30º ± Regular Φ 4 mm - 45º ± 3.37 Regular Φ 4 mm - 55º ± The higher torsional rigidity for hybrid composite wires as compared to the single rods used in their packing was due to the higher polar area moment of inertia (Eq. (4.5)). The effect of the rod diameter used in the pack, upon the torsional rigidity of hybrid composite wires was also found to be highly significant as the rod diameter was doubled from 2 mm to 4 mm, due a significant increase in polar moment of inertia (nearly 16 times). 101

103 Mechanical Testing and Characterisation of Hybrid Composite Wires The effect of braid angle in torsion was observed to be significant, unlike in flexure. When the braid angle was increased from 30 to 45, an increase in torsional rigidity of 13.1% was observed, for hybrid composite wires with Ф 2 mm rods and diamond braid topology. As the braid angle was further increased from 45 to 55 a decrease in torsional rigidity of 18.2% was observed. A similar trend, but change in percentage change was observed for hybrid composite wires with Ф 4 mm rods and diamond braid topology, where an increase in torsional rigidity of 9.1% was observed as the braid angle was increased from 30 to 45. However, as the braid angle is further increased from 45 to 55 a decrease in torsional rigidity of 8.2% was observed. If this trend is observed for hybrid composite wires with Ф 4 mm rods, for regular braid topology, an increase of 2.2% was observed as the braid angle was increased from 30 to 45, and a decrease of 8.7% as the angle was further increased from 45 to 55. The highest torsional rigidity of 45 braid conforms to the trend observed analytically among composite cross-ply laminates predicted in composite laminate theory [131] which predicts the highest in-plane shear modulus (G12) by 45 ply orientation followed by 30 and 55 ply orientations. A study conducted in [132] on biaxial braided composite tubes, determined the effect of braid angle upon torsional properties of biaxial braided composite tubes, where the 45 specimens showed the highest shear modulus among two other braid angles of 31 and 65 investigated. In addition, in a study conducted in [105] on braided pultruded composites (method of production shown in Chapter 2), 45 braided specimens showed the highest shear modulus followed by 30 and 55 braided specimens. The effect of topology on the torsional rigidity of hybrid composite wires with Ф 4 mm rods was also observed, where the regular braid topology among all three braid angles (30, 45 and 55 ) investigated was observed to be higher than diamond braid topology. An increase in torsional rigidity of 19.2% at 30, 13.4% at 45, and 12.5% at 55 braid angle was observed as the braid topology was changed from diamond to regular. 102

104 Mechanical Testing and Characterisation of Hybrid Composite Wires 45 braid depicting stiffest response as compared to other braid angles to maximum shear resistance Concavo-convex behaviour showing an increase in torsional rigidity with decreasing rate followed by an increasing rate, due to stiffening effect of the braid 55 braid angle with diamond braid topology, showing an increase in torsional rigidity with a decreasing rate. The rate is expected to increase at higher twist angles. (a) Figure 4.8: Torsional behaviour of hybrid wires and individual rods for: (a) Ф 2 mm rods and (b) Ф 4 mm rods (b) 103

105 Mechanical Testing and Characterisation of Hybrid Composite Wires This trend of increase in torsional rigidity as the topology is switched from diamond to regular can be explained using the braid crimp values (depicted in Table 3.1) which are lower in the case of the regular braided structures, providing lower extensibility, resulting in higher rigidity values as compared to diamond braided structures, when the same number of bobbins (24 bobbins used) is employed for producing the braid. As observed in Figure 4.8, none of the specimens tested underwent any form of failure. As stated above both hybrid composite wires (with Ф 2 mm rods and Ф 4 mm rods), depicted highest torsional rigidity (slope) with 45 braid angle followed by 30 and 55 braid angles. The torsional behaviour (apart from the elastic response) was observed to be different for both types of hybrid composite wires (with Ф 2 mm rods and Ф 4 mm rods), maximum test limit of 400 /m. Whilst the hybrid composite wires with Ф 2 mm rods, showed linear behaviour, the wires with Ф 4 mm rods depicted a non-linear behaviour. As, observed in Figure 4.8, the hybrid composite wires Ф 4 mm rods, 55 braid angle and diamond braid topology, as the angle of twist was increased, the torsional rigidity also increased but at a decreasing rate. For all other configurations of hybrid composite wires studied with Ф 4 mm rods, concavo convex curves were observed (with reference to x axis). This form of curve implies that with an increase in angle of twist, the torsional rigidity initially increases at a decreasing rate, followed an increasing rate. This increase in torsional rigidity with at increasing rate was due to the stiffening effect of the braid at higher twist angle. The reason why this concavo-convex pattern was not observed for 55 braid could be due to the delay of the stiffening effect which might come into action at a higher twist angle (> 400 /m) as the stiffening effect started first for the 45 braid, then by the 30 braid, and then by 55 braid for hybrid composite wires with regular braid topology. The non-linear behaviour of all configurations of hybrid wires with Ф 4 mm rods, could have arisen due to the inter-rod interaction (wrapping of surrounding rods around the central rod), resulting in geometric non-linearity. The behaviour of single rods can also be observed in Figure 4.8, where the rods depicted linear behaviour till 104

106 Mechanical Testing and Characterisation of Hybrid Composite Wires the maximum tested limit (400 /m). The fibre reinforced composite rods are expected to depict non-linear before failure, as the unidirectional fibres in composite rods depict inelastic behaviour in a shear mode of deformation at very high strains that has been shown in [10] Comparison of hybrid composite wires with traditional metallic armour wires The great potential of carbon fibre reinforced polymer composites has been proved in literature [3-6] to be a promising alternative in replacing metallic tensile and hoop armours. These composites show higher tensile strength and fatigue and enable significant overall weight reduction of flexible riser systems. A comparison of hybrid composite wires has been made with metallic wires in this section using properties such as: corrosion, the flexural & torsional stiffness, and their behaviour under external pressure (when incorporated into the riser) Corrosion The limitations of flexible risers due to the poor corrosion properties of metallic tensile armour wires from H 2 S and CO 2 has been described in detail in the literature review (Page 32). In this comparison the corrosion resistance of carbon fibre reinforced polymer composites due to H 2 S and CO 2, has been determined to be excellent in literature [80], proving the advantages of using hybrid composite wires in comparison with metallic armour wires. The over-braid sleeve (with Dyneema fibres) in the hybrid composite wires, too offers excellent corrosion resistance, as the Dyneema fibres are chemically inert Flexural and torsional stiffness The different torsional and flexural rigidities for different structures has been shown in Figure 4.9. The flexural and torsional rigidities of metallic structures have been determined analytically using Eqs (4.1) & (4.5). The tensile and shear modulus that 105

107 Mechanical Testing and Characterisation of Hybrid Composite Wires are essential for determining the flexural and torsional rigidities of metallic (carbon steel) structures, were obtained from literature. The axial modulus of carbon steel was found to be 210 GPa that has been obtained from [133], and the shear modulus of carbon steel was found to be and its shear modulus value of 79 GPa was obtained from [134]. For easier comparison of hybrid composite wires with metallic counterparts, the flexural and torsional rigidities of configurations of hybrid composite wires, with same individual rod diameters have been averaged. (a) (b) Figure 4.9: Comparison between different structures using: (a) flexural rigidity and (b) torsional rigidity Comparison with traditional metallic tensile armour wires. The comparison of hybrid composite wires was made with the traditional armour wires, which have a rectangular cross-section. The dimensions of these wires (30 mm X 1.5 mm) have been provided in [135]. It should be noted for riser curvatures, the 106

108 Mechanical Testing and Characterisation of Hybrid Composite Wires thickness and the width of these traditional armour wires could be higher. On comparing the flexural rigidity between the hybrid composite wires with Ф 4 mm rods and the traditional metallic wire, an increase of nearly 389% was observed, whilst the flexural rigidity of hybrid composite wires with Ф 2 mm rods was found to be 68% lower than the traditional armour wire. In case of torsional rigidity, both of the hybrid composite wires (with Ф 4 mm rods and with Ф 4 mm rods) showed a substantial decrease when compared with torsional rigidity of traditional metallic wires. A decrease of 98% was observed for wires with Ф 4 mm rods, and 99.9% for wires with Ф 2 mm rods Comparison with metallic structures with similar dimensions If the flexural and torsional rigidities of hybrid composite wires are compared with metallic structures with similar dimensions, a in decrease of ~ 96% in case of both flexural and torsional rigidity was observed if the hybrid composite wires with Ф 2 mm rods are compared with metallic circular rod with Ф 6 mm (similar cross-sectional area). A similar decrease of ~ 95% was observed for both torsional and flexural rigidities when a comparison was made between hybrid composite wire with Ф 4 mm rods and a circular metallic rod with Ф 12 mm Behaviour under through thickness compression During service, the riser is subjected to radial compressional forces due to external pressures. This external pressure may cause the rearrangement of the hexagonal packed rods inside hybrid composite wires, if the braid angle is low (observed in Figure 4.3a), in this aspect the traditional metallic wires and have a solid profile, and will have much higher through thickness compressive strengths. Therefore, as observed from the flexural tests conducted on the hybrid composite wires, a high braid angle (like a 55 braid angle) with a diamond braid topology can be chosen so that would ensure integrity of the hexagonal pack even at very high curvatures. The high hoop pressure exerted by the over-braid sleeve at high braid angles and diamond braid topology impart high through thickness compressive strengths. 107

109 Mechanical Testing and Characterisation of Hybrid Composite Wires 4.4. Summary Reflecting upon the experimental work carried out in this chapter, the key concluding points are: The structural (rod diameter, braid angle and braid topology) properties of hybrid composite wires can be changed, depending upon the riser curvature. The effect of braid angle (30, 45 and 55 ) and braid topology (diamond and regular) upon the flexural rigidity of the hybrid wire was found to be considerable but inconclusive. However, these parameters did have a significant effect in torsion. The effect of both braid angle and braid topology was more pronounced during higher deformation loads (torsion and flexural). The hybrid wires with bonded edges showed almost twice the flexural rigidity compared to those with no bonded edges, helping inferring that the flexural rigidity of these wires will be higher near the riser ends (end-fitting). If the flexural behaviour of single rods are compared with hybrid composite wires they are used in. The hybrid composite wires show non-linear behaviour under both flexural and torsional deformations with the help of inter-rod interactions, helping to prevent brittle elastic fracture. The hybrid composite wires with Ф 2 mm rods depicted significantly lower flexural and torsional rigidities as compared to traditional metallic armour wires, with an advantage of being 4 times thicker than the metallic armours which could possibly eliminate the problem of double cross-winding. It is also essential to use higher braid angles in hybrid composite wires, ideally with diamond braid topology, to improve their in-through thickness compressive strengths 108

110 Multi-scale Modelling of Hybrid Composite Armour Wires Multi-scale Modelling of Hybrid Composite Armour Wires A multi-scale model for the hybrid composite wires, using a combined analytical and computational approach has been presented in this chapter. This approach provided a simpler and computationally less expensive solution to modelling an otherwise complex structure of the hybrid composite wires. The multiscale model has been developed to understand the role of the varying structural parameters of overbraid sleeve on the torsional and flexural behaviour (elastic) of hybrid composite wires. The multi-scale model has been used for all configurations of hybrid wires with Ф 4 mm rods Introduction The methodology used for multiscale modelling technique for modelling hybrid composite wires, has been shown in Figure 5.1. In the multiscale model, the braid has been modelled as a homogenous orthotropic shell, while the composite rods, as homogenous transverse isotropic. The homogenised macro-mechanical properties of composite rods and the braid shell were obtained using analytical models from literature, using micro- and meso-mechanical properties of their constituents. The friction acting between the individual rods, the rods and the over-braid, has been accommodated in the model along with the pre-tension in braid tows (arises during braiding stage), in form of an equivalent hoop pressure exerted by the braid shell on the rod bundle. The torsional and flexural behaviour (elastic) of hybrid wires has been studied for small displacements using multi-scale model. The reason for referring the modelling technique as multi-scale, is because different scales (micro & meso) are used to determine the macro structural homogenised elastic property of hybrid composite wires. 109

111 Multi-scale Modelling of Hybrid Composite Armour Wires Composite rods Braid shell Finite Element Model Macro-structural elastic properties of composite rod Macro-structural Analytical elastic properties model of braid shell Micro-mechanical analytical model Meso-mechanical analytical model Composite rod Diamond braid Regular braid Fibres Matrix Meso-structural properties (Braid unit cell s geometrical and structural properties) Micro-structural properties (Fibre & matrix, physical and elastic properties and composition) Micro-structural properties (Physical, and elastic properties of fibres) Figure 5.1: Schematic representation of the process for multi-scale modelling of hybrid composite armour wires 110

112 Multi-scale Modelling of Hybrid Composite Armour Wires An alternate approach could also be used, which would require modelling the braid and the packed rods as it is, implying creation of a replica of the hybrid wires. This technique could be carried out by geometric and structural modelling the braid tows with packed rods (as core) in computer aided design (CAD) software, then importing the formed parts into a finite element modelling software. This approach would require precise dimensions (tow width, tow thickness, and braid crimp) of the braided tows and perfect contact (no intersection or gaps) between braid tows. A perfect contact between braid tows and packed rods will also be needed. The execution of this technique for finite element modelling would be computationally highly expensive and complex. Moreover each braid configuration is different from the other (different braid angles and topology result in different tow dimensions). If this technique is compared with the multiscale modelling technique introduced in this chapter, the computation cost and complexities associated with modelling hybrid composite wires will be reduced significantly. The multi-scale model incorporates all meso geometric and structural parameters (braid angle, braid topology, braid crimp, dimensions of braid tows) providing a good agreement with experimental test results, without modelling the complex geometry of braid itself for every hybrid wire configuration Methodology for multiscale modelling A detailed description of extrapolation of homogenised macro-mechanical elastic properties of composite rods and braid shell has been described in this section Elastic properties of composite rods The solid unidirectional composite rods, stacked in form of hexagonal closed pack were considered to be a transversely isotropic in nature. As a result of transverse isotropy the 1-2 and 1-3 planes mutually perpendicular to the 2-3 plane (see material coordinates in Figure 5.2) will be in isotropy with each other resulting in same elastic properties. 111

113 Multi-scale Modelling of Hybrid Composite Armour Wires Figure 5.2: Schematic representation of material coordinates of pultruded composite rods, with fibre axis as 1 direction Table 5.1: Elastic properties of fibre and matrix in the composite rod found from literature [with references] Type E11 G12 ν12 (GPa) (GPa) Carbon Fibre 230 [136] 24 [136] 0.27 [136] (T700) Vinyl Ester 2.9 [137] 1.17 [138] 0.35 [138] E 22 = E m(1 + ξηv f ) (1 ηv f ) (5.1) η = E f E m 1 E f E m + ξ ν 12 = V f. ν f + V m. ν m (5.2) ν 21 = [V f. ν f + V m. ν m ] E 22 E 11 (5.3) G 23 = K m = K f = E 22 (1 ν 23 ) E m 3(1 2ν m ) 3 E 11f E 22f E 33f 3 3(1 2 ν 12f ν 13f ν 23f ) (5.4) (5.5) (5.6) 112

114 Multi-scale Modelling of Hybrid Composite Armour Wires K = [ V f + V 1 m (5.7) ] K f K m ν 23 = 1 ν 21 E 22 3K (5.8) The values of E11 and G12 were determined experimentally, by closely following ASTM D3916 [123], and have been reported in Table 5.2. The remaining elastic properties (E22, E33 G23, ν12, ν13, and ν23), of unidirectional composite rods were calculated, using the equations (5.1) to (5.8), mentioned in [127, ], with help of fibre volume fraction (Vf), and the elastic properties of fibre and matrix (reported in Table 5.1). The bulk modulus of transverse isotropic fibres (Kf) can be quantified using Eq. (5.6) obtained from [142], and for isotropic matrix (Km) using Eq. (5.5). The value of ν23 of 0.29 was used for carbon fibres was obtained from [136]. Table 5.2: Elastic properties of composite rods E11 E22 E33 G12 (GPa) (GPa) (GPa) (GPa) ± ± 0.10* 1.65* * Experimentally determined G13 G23 ν12 ν13 ν23 (GPa) (GPa) The experimentally determined values (as stated in Chapter 4) of E11 and G12 were lower than the calculated values, due to the presence of voids, deformed fibres, twisted fibres and miss-aligned fibres (shown on Pg. 57) observed from microscopic analysis. Although higher values of G23 were obtained for composite rods (as analytical equations were used), in comparison with G12 and G13, the overall effect of G23 on flexural and torsional mechanical properties of hybrid composite wires was found to be insignificant. 113

115 Multi-scale Modelling of Hybrid Composite Armour Wires Braid shell properties: meso-mechanical analytical model The biaxial over-braided sleeve was modelled as a 3-D orthotropic shell. The quantification elastic properties of braid is relatively complex as compared to composite rods, since the elastic properties of the braid will be not be same as the property of the individual fibre tows used to produce over-braid sleeve. There are several experimental studies and theoretical models present in literature [ ] with regard to biaxial braids with and without a core. However, none of these studies can predict all nine engineering elastic constants for a given braid angle and braid topology. Finite element modelling of an orthotropic 3-D shell requires nine elastic engineering constants. In this context, an alternate technique was adopted using an analytical approach presented by Byun, 2000 [148] for triaxial braided composite. The triaxial braid is different from a biaxial braid as it has additional set of tows along the braid axis. These tows lie in between the biaxial tows, and are kept straight during the braiding process. This analytical model proposed by Byun, 2000 [148] predicts 3- D engineering constants for a triaxial braided composite for any given braid angle by combining stiffness s of axial tows, biaxial tows and matrix. In order to translate the triaxial braided composite model into a dry fibre biaxial braid shell, the stiffness properties of axial tows and matrix were assumed to be zero, resulting in stiffness contribution only from biaxial tows. Table 5.3: The properties UHMW-PE fibres and HD-PE matrix Type E11 (GPa) G12 (GPa) UHMW-PE fibres 116 [128] 0.95 [129] 0.29 [149] HD-PE matrix 0.70 [150] 0.25 [151] 0.40 [152] ν12 In order to calculate the homogenised elastic properties of the triaxial braided composite, the model [148] first transforms the stiffness matrix of a fibre tow by incorporating the crimp angle, followed by transforming the transformed stiffness matrix of the fibre tow (inclusion of crimp), by including the braid angle ± θ, which 114

116 Multi-scale Modelling of Hybrid Composite Armour Wires the tow makes with the braid axis (imaginary vertical axis along the length of braid). This transformed stiffness matrix that includes the crimp angle and the braid angle is then used for calculating the stiffness of the braid, by including the structural parameters of braid found experimentally, as represented in Eq. (5.9), where S ij bp and S ij bm, are compliances of biaxial tows at a particular braid angle (S ij bp for +θ and S ij bm for -θ). The other terms in Eq. (5.9): S a ij and S m are compliances of axial tows and the matrix whereas, V b is the volume of biaxial tows, V a is volume of axial tows, V t is the total volume of the braid unit cell, and V y is the matrix volume fraction. The compliance matrix for triaxial braided composite can then be used to obtain the required engineering constants. For the biaxial over-braid sleeve, Eq. (5.9), can be rewritten as Eq. (5.10). V b V b S ij = [( V a a V t S ) + ( bp ij 2V t S ) + ( bm ij 2V t S ) ij i, j = 1, 2, 3, 4,5, 6 (5.9) + ( 1 V 1 y S m )] V b V b S ij = [( bp 2V t S ) + ( bm ij 2V t S )] ij 1 i, j = 1, 2, 3, 4, 5, 6 (5.10) E 11 = 1 ; E S 22 = 1 ; E 11 S 33 = 1 ; 22 S 33 G 23 = 1 ; G S 13 = 1 ; G 44 S 12 = 1 ; 55 S 66 (5.11) ν 12 = S 12 ; ν S 13 = S 13 ; ν 11 S 23 = S 23 ; 33 S 22 A detailed mathematical calculation of braid structural parameters like: crimp angle, percentage of axial and biaxial tows, have been presented by Byun [148]. But since, 115

117 Multi-scale Modelling of Hybrid Composite Armour Wires these parameters are interlinked and incorporate dimensions of axial tows, and volume of axial tows in the braid unit cell, the mathematical calculations were not used, due to the biaxial nature of over-braid sleeves. Instead, the crimp, and volume of biaxial braid was determined experimentally, giving greater accuracy of results. A MATLAB [153] code was written (script shown in Appendix Pg. 185) for the equations presented in [148], to extrapolate the elastic properties of braid sleeve, which have been presented in Table 5.5. The process of measurement of volume of biaxial tows in a unit cell and the total volume of unit cell using analytical equations has been quantified in Appendix (Pg. 178). The model in [148] assumes the fibre tows as unidirectional composite rods. As stated above, the model first determines the elastic properties of the fibre tow, before crimp and its structural properties in braid are implemented. Therefore in order to determine the elastic property of the fibre tows before the crimp and structural properties of braid are incorporated, a weak matrix of high density poly-ethylene (HD-PE) has been assumed only between the fibres in the tow. The matrix outside the fibre tows has been assumed to be absent. The elastic properties of UHMW-PE fibres and HD-PE matrix have both been reported in Table 5.3, where the axial modulus of HD-PE is 165 times lower than fibre axial modulus and its in-plane shear modulus roughly 4 times lower than the fibre s in-plane shear modulus. Apart from its weak mechanical properties, HD-PE was also chosen because it was poly-ethylene based, just as the fibres in the braid. The choice of HD-PE also helped in providing good agreement between experimental and multi-scale model behaviour in flexure and torsion. The fibre volume fraction value of: 0.70 in the tow was assumed i.e, before crimp and braid structural properties were implemented, to determine the elastic properties of braid shell. Although maximum possible fibre volume fraction of 0.90 (hexagonal pack) and 0.78 (square pack) could also be chosen, but that would imply the fibres in the tow are in contact with each other. As this stage closely represents the tow that is wound onto the bobbin before braiding, the winding process is expected to create micro gaps between the fibres in tow. Therefore a slightly lower volume fraction of 116

118 Multi-scale Modelling of Hybrid Composite Armour Wires 0.70 has been chosen, that also helped in providing good agreement between multiscale model behaviour and experimental results in both torsion and flexure. The value of fibre volume fraction of 0.70 was also assumed on the basis of a simple calculation, where the cross-sectional geometry of Dyneema tow (on the bobbin) before braiding was assumed to be rectangular (tape). The area of the cross-section of the tow with width 4 ± 0.02 mm (measured using image analysis) and thickness of ± mm (measured using Vernier Calliper), the area of the tow prior to braiding was found. The area occupied by 780 fibres in a tow was also found, and divided with total area of the tow. The fibre volume fraction of was determined. This value was rounded off to 0.70, and was used as representative of fibre volume fraction of the Dyneema tow. It should also be noted that similar torsional and flexural rigidities of hybrid composite wires through multi-scale modelling were found, when the fibre volume fraction in the tow was assumed between 0.65 and The fibre volume fraction of the braid at different braid angle, once the braid crimp and braid structural properties (in form of braid angle and volume of biaxial tows), will be lower than 0.70, as the in that case the inter-tow spacing in the braid is also incorporated. Using the properties of fibre and matrix, and the fibre volume fraction, the elastic properties of fibre tows with weak matrix were computed using Halpin & Tsai equations and other equations ((4.6),(4.7), (5.1) - (5.8)). The value of ν23 for fibre, that has been used to calculate the bulk modulus (K), and the value of G23, of the tow was obtained from literature [154] from similar Dyneema fibres as 0.2. The elastic properties of UHMW-PE tow has been calculated in Table 5.4. Table 5.4: Calculated properties of UHMW-PE tow E11 E22 E33 G12 G13 G23 ν12 ν13 ν23 (GPa) (GPa) (GPa) (GPa) (GPa) (GPa)

119 Multi-scale Modelling of Hybrid Composite Armour Wires The elastic properties of over-braid (modelled as shell) extrapolated from the analytical model, have been reported in Table 5.5. The elastic constants of the braid shell have been represented as per the material coordinate system represented in Figure 5.3, where E 11 is the axial modulus of braid sleeves (in direction of braid axis) and G 12 is the in-plane shear modulus. If the values of axial modulus are observed for different braid angles, an increase in braid angle led to a decrease in axial modulus, which is expected, since a lower braid angle is closer to the load axis (in a uniaxial tensile test). The effect of braid topology on axial modulus was also observed, where regular braid topology depicted higher axial modulus due to lower crimp angle and float length. The presence of crimp in braid sleeve, imparts it extensibility; higher crimp values as in case of diamond braid topology, offers higher extensibility to the braid, thereby reducing resultant stiffness of sleeve as compared to regular braid topology. A decrease in the Poisson s ratio (in 1-2 direction) with an increase in braid angle was also expected, since an increase in braid angle increases the longitudinal strain and decreases transverse strain. The shear stiffness values, especially in (1-2 direction) did not yield the expected trend. An increase in braid angle led to a decrease in shear stiffness, which is expected to be highest for a 45 braid angle, followed by 30 and 55 braid angle as reported in [131]. The reason for this unexpected trend is due to the sensitivity of the analytical model towards crimp angle, which increases with an increase in the braid angle. 118

120 Multi-scale Modelling of Hybrid Composite Armour Wires Table 5.5: Elastic properties of different configurations of braid shell in hybrid composite wire with Ф 4 mm rods, using analytical model Type Braid Angle (⁰) Topology E 11 (GPa) E 22 (GPa) E 33 (GPa) G 12 (GPa) G 13 (GPa) G 23 (GPa) ν 12 ν 13 ν Diamond Diamond Diamond Regular Regular Regular

121 Multi-scale Modelling of Hybrid Composite Armour Wires Computational modelling: finite element model The elastic properties obtained for braid shell and composite rods using analytical models have been used in the finite element package: Abaqus CAE 6.14 [155] to determine the behaviour of the multi-scale model when subjected to twist and flexure Geometry and mesh In the finite element package, circular composite rods and the braid shell were formed. All parts were assembled as shown in Figure 5.3c, where material coordinates have also been depicted. 3 n n (a) (b) (c) Figure 5.3: (a) Material orientation for composite rod, (b) material orientation for shell, and (c) mesh for the model Rectangular co-ordinates were chosen for the composite and braid shell, with axial direction (represented as 1) along the model length. The transverse direction (represented by 2) and out of plane direction (represented as 3 for composite rod and as n for the shell) of both composite rod and shell have also been shown in Figure 5.3b. If cylindrical coordinates are chosen for composite rods, the results obtained will 120

122 Multi-scale Modelling of Hybrid Composite Armour Wires be exactly the same as the results from rectangular co-ordinates for every type of simulation carried out. Also in order to keep the coordinate system consistent for both composite rods and braid shell, rectangular co-ordinates were chosen. The element type chosen for shell was a S4 element, which is a 4 node element for a general purpose shell, as they use thick shell theory when the shell thickness is high in comparison with the length of the element, and become discrete Kirchhoff thin shell elements when the corresponding thickness decreases. This implies that the transverse shear deformation will be taken into consideration, if the shell thickness is high, and assumed to be zero of the shell thickness is very low. The thickness of the shell is considered to be high (considering transverse shear deformation) if the thickness to length ratio crosses 1:15, as stated in Abaqus manual 6.14 [156]. For the composite rod, C3D8 element was chosen which is 8 node brick element (hexahedral mesh). A hexahedral mesh was chosen as it offers numerical advantages [157], offers higher accuracy in case of regularity, angle distribution and anisotropy [158]. It is a useful meshing technique for linear static bending, and linear static torsion type of analysis [159]. Since the edges of the composite rods are in contact with the adjacent rods, a uniform brick element along the circumference of circular crosssection was used. Same type of mesh was also used for both three point and four point flexural test simulation in Abaqus CAE to maintain consistency Mesh sensitivity study The mesh density sensitivity was conducted on the hybrid wire assembly, instead of conducting it separately for composite rods and braid shell, due to the multiple components of composite rods (7 rods in the assembly), an increase in number of mesh elements in the composite rod would result in an increase in number of elements by 7 times, thereby increasing the computation time significantly. The number of elements along the shell, were dependent upon the number of elements along the length of rods, in order to keep the length of elements same for both the rods and the shell. 121

123 Multi-scale Modelling of Hybrid Composite Armour Wires Increasing mesh density Figure 5.4: The different number of elements used to carry out the mesh sensitivity study on multiscale model for hybrid composite wires with Ф 4 mm rods Likewise, the number of mesh element was increased incrementally along the edges of the rods, from the lowest possible keeping the element aspect ratio within the recommended range mentioned in Abaqus manual 6.14 [159]. The incremental increase in elements (shown in Figure 5.4) along the edges also determined the width of elements in the shell, to make sure each element of the shell, along the filleted edges which were in direct contact with the composite rods perfectly overlapped each other. The recommended aspect ratio (length is to thickness) of a hexahedral mesh recommended in Abaqus manual 6.14 [159], is 1:10. From the mesh sensitivity study carried out the number of elements for flexural mode of deformation, were equal to 275,420 while, for torsion mode of deformation number of elements were chosen were equal to 155,876. Although higher number of mesh elements could be chosen (507,600 for flexural and 287,280 for torsion), it was found to be highly computationally expensive, yielding an increase in flexural and torsional rigidities of about only 1% or less. 122

124 Multi-scale Modelling of Hybrid Composite Armour Wires 33,782 87, , ,280 59, , , ,600 Figure 5.5: Mesh density sensitivity study for flexural and torsional mode of deformation for hybrid wire assembly with Ф 4 mm rods Interaction properties In order to understand the mechanical behaviour of hybrid composite wire through multiscale model, it is vital to know the coefficient of friction acting between the composite rods (µr) and also between the braided fibres (modelled as shell) and the rods (µs). The pultruded rods had a matrix rich layer at the circumference as shown in Figure 5.6, as result the friction behaviour of the pultruded rods was dictated by the matrix rich layer. The coefficient of friction between solidified vinyl-ester resin is approximately equal to 0.49 [160], and has been used as the coefficient of friction value between the composite rods. The coefficient of friction value for UHMW-PE fibres is known to be very low, giving it excellent abrasion resistance. The value of µs was found using Eq. (3.16), to be equal to ± (explained using Figure 3.16) using tow tensions (T0 & T0 ) and wrap angle (γ). A parametric study has also been 123

125 Multi-scale Modelling of Hybrid Composite Armour Wires conducted to determine the effect of friction upon flexural and torsional rigidity of hybrid wires in the Chapter 6. Matrix rich layer Figure 5.6: Micrographs of cross-section of composite rod with Ф 4 mm, showing matrix rich circumference For normal behaviour, between the composite rods and between shell and rods, hard contact was used. The normal behaviour according to Abaqus manual [159], determines the type of contact and the normal behaviour between the master and slave surfaces. The hard contact relationship minimizes the penetration of the slave surface into the master surface at the constraint locations and does not allow the transfer of tensile stress across the interface. Practically, the braid exerts constant and uniform hoop pressure on the packed rods, and is highly pivotal in maintaining the structural integrity of the hybrid composite wires. The pressure exerted by the braid shell, is largely determined by how tight the braid is, such that the tighter the braid is, higher the grip braid will have on the packed rods, due to higher hoop pressure. The tightness of the braid, in form of tow tension, can be set during the braiding process, by adjusting the spring tensioner of the bobbin carriers on the braiding machine. Hence, an additional load step was introduced, where hoop pressure was incorporated into the model. The hoop pressure (p 0 ) was calculated using Eq. (5.12) presented in [161], which has been modified for a single biaxial braid layer (as in case of overbraid in hybrid wires). This equation is applicable to filament wound structures and is similar to the hoop pressure equation for braided structures [162]. 124

126 Multi-scale Modelling of Hybrid Composite Armour Wires p 0 = [ Tsin2 θ r 1 w ] + [Tsin2 θ r 2 w ] (5.12) p 0 = [ πtsin2 θ (rπ + 6r)w ] + [ 2πTsin 2 θ (2πr + 12r + tπ)w ] (5.13) The Eq. (5.12) is applicable to circular cross-section, where the hoop pressure (p0) can be calculated with the help of tow tension (T), braid angle (θ), tow width (w) of the biaxial braid sleeve, the distance from the centre of the core to the mid thickness of biaxial sleeve (r 1 ), and radius of the core (r 2 ). The Eq. (5.12), has been modified to suit the cross-section of hybrid wire (hexagon with filleted edges) in form of Eq. (5.13), where the hoop pressure can be calculated using tow tension (T), tow width (w), braid angle (θ), braid thickness (t) and radius of the individual rod (r). The tension (T), in Eq. (5.12) & (5.13), is the tension of the tow just before braiding calculated in Chapter 4. Table 5.6: Hoop pressure values for different braid configuration Φ (mm) Braid angle (⁰) Topology Hoop pressure (MPa) 4 30 Diamond Diamond Diamond Regular Regular Regular 0.09 The hoop pressure values for different configurations of braids have been reported in Table 5.6. The 55 braid angle in both braid topologies and in both packings (with Φ 2 mm and Φ 4 mm rods) exerted maximum hoop pressure, although it has the lowest braid tension, due to its lowest tow width (as reported in Table 3.1), which plays a pivotal role in determining the hoop pressure value. The same reason can also be used 125

127 Multi-scale Modelling of Hybrid Composite Armour Wires to explain the higher hoop pressure in case of diamond braid topology, which had lower tow width as compared to regular braid topology Boundary conditions The hoop pressure in multi-scale model was applied as a pre-load condition, that ensured contact be established between the different components in the model. The braid shell and the rods surrounding the central rod were allowed to move in the 1-2 plane, but were constrained along the model length direction (model axis depicted in Figure 5.8). On the central rod, a boundary condition of encastre was applied, constraining all degrees of freedom. As a result of hoop pressure, a contact was established between the composite rods, and between the composite rods and the braid shell, which in absence of hoop pressure was not feasible. The displacements encountered by the braid shell, and the surrounding rods in the rod bundle due to hoop pressure, have been shown in Figure 5.7, where central rod shows no displacements, since all degrees of freedom were constrained. The hoop pressure was maintained in the following load step, which involved application of twist (in case of torsion) or downward displacement (in case of flexure). The boundary condition of encastre was removed during the load step. (a) (b) Figure 5.7: Hoop pressure (po) applied on the braid shell, and (b) displacements (in mm) encountered by rods due to applied hoop pressure 126

128 Multi-scale Modelling of Hybrid Composite Armour Wires For torsion, the length of the model used was the same as the experimental length of 100 mm. In order to apply a twist to the model, kinematic coupling was used. Using kinematic coupling, the boundary condition was applied to the two reference nodes, each opposite to both cross-sectional ends of the model. On the first reference node, a twist of 3 /m (0.3 ) was applied, constraining the rest of degrees of freedom, except along the model length. On the second reference node, encastre boundary condition was applied. (a) (b) 127

129 Multi-scale Modelling of Hybrid Composite Armour Wires (c) Figure 5.8: Schematic representation of boundary conditions on the multi-scale model in case of: (a) torsion, (b) three-point flexure, and (c) four-point flexure tests. In the case of flexural mode, the length of the model was 176 mm i.e., half the experimental span length of 352 mm, due the symmetry along the cross-section of the model. The use of the load and support pin (used in the experimental set-up) was avoided, for both the three and four point test simulations to reduce the number of contact points and number of elements, thereby reducing complexities and computation cost. Moreover, as the hoop pressure is applied on to the shell, both shell and the composite rods come in contact with each other, leading to displacements as shown in Figure 5.7. If the load and support pins are used the contact established between them and the hybrid composite wires will be lost. For the three point bend simulation, a downward displacement of 2.5 mm (0.25 m -1 curvature) was applied at the top edge of the shell in contact with the load pin (experimentally), as shown in Figure 5.8b. The cross-section at one end of the model (mid-span) was constrained along the length direction (to avoid the rods escaping the shell or vice-versa). On the other end of the model, in contact with the support pin (experimentally), the entire cross-section was constrained in the sideways direction, to avoid sideways movement of the model. The same boundary conditions were applied for the four point flexural test simulation as used in three point simulation, 128

130 Multi-scale Modelling of Hybrid Composite Armour Wires with an exception on the location where the deflection was applied. The downward deflection of 2.0 mm was applied onto the top face of the shell at half model s length (experimentally half of mid-span), as shown in Figure 5.8c. The downward displacement of 2.0 mm applied resulted in a displacement of ~ 2.5 mm at the midspan (curvature of 0.18 m -1 ) Results and observations The experimental and behaviour from finite element model for single rods (and bundled rods in case of torsion) will be described in this section. For hybrid composite wires, the multi-scale model was used to investigate the effect of the structural parameters of the over-braid sleeve on the flexural and torsional behaviour of the hybrid composite wires. Two different pre-load conditions were considered: (a) with the equivalent hoop pressure and (b) without the equivalent hoop pressure applied by the over-braid sleeve on the rod bundle by using the interaction properties and the equivalent hoop pressure discussed in the previous sections Torsional behaviour The experimental behaviour of hybrid composite wires and the behaviour from multiscale model, for different braid configurations have been shown in Figure 5.9. As observed in Figure 5.9, a close agreement was found between experimental and multiscale model behaviour, with a maximum deviation of 5.9%, for 30 braid angle with diamond braid topology, with applied hoop pressure. The torsion tests as described in Chapter 4, showed that among different types of hybrid wire configurations the highest torsional rigidity (slope of moment and twist per length) and was portrayed by a 45 braid angle followed by 30 and 55 braid angles. The highest torsional rigidity of 45 braid conforms to the trend predicted by composite laminate theory, that predicts highest in-plane shear modulus (G12) by 45 ply orientation followed by 30 and 55 ply orientations [131]. A study conducted in [132] to determine the effect of braid angle upon torsional properties of biaxial braided 129

131 Multi-scale Modelling of Hybrid Composite Armour Wires composite tubes, 45 specimens showed the highest shear modulus among two other examined braid angles of 31 and 65. In addition, in a study conducted in [105] on braided pultruded composites, 45 braid showed the highest shear modulus followed by 30 and 55 braids. The effect of topology was also observed to be significant, as the hybrid wires with regular braid depicted higher torsional rigidities, for all three braid angles, as compared with hybrid wires with diamond braid topology, due to the lower crimp values (shown in Table 3.1). The effect of braid angle using multiscale model was found to be significant, where 30 braid angle depicted highest torsional rigidity (steepest slope) followed by 45 braid and the 55 braid angle, among both diamond and regular braid topologies. This was partly in contradiction with experimental behaviour, where 45 braid depicted highest torsional rigidity followed by 30 and 55 braid angles. The highest torsional rigidity for 30 braid angle using multiscale model, was a result of highest (in-plane) shear properties predicted in Table 5.5, followed by 45 and 55 braid angles, which as cited above is due to sensitivity of the analytical model towards crimp angle, that increases with an increase in braid angle. 130

132 Multi-scale Modelling of Hybrid Composite Armour Wires Figure 5.9: Experimental and FE behaviour of hybrid composite wires under torsion 131

133 Multi-scale Modelling of Hybrid Composite Armour Wires The multiscale model however, was successful in capturing the effect of braid topology, where the regular braid at all three braid angles, depicted higher torsional rigidity as compared to diamond braid topology, in agreement with experimental behaviour. The stress distribution in hybrid wires, due to torsion can be observed in Figure 5.10, where the effect of hoop pressure can also be observed, at 3 /m twist. The different stress distribution pattern on the rods and the braid shell can be observed for both cases: one without any hoop pressure (Figure 5.10a) and one with hoop pressure (Figure 5.10b). Due to the hexagonal packing of the rods, when the twist is applied on one end of the model while the other end is fixed, the twist causes the central rod to rotate on its axis, while the surrounding rods wrap around the central rod. In Figure 5.10a (hoop pressure absent), as explained above (in case of twist of rod bundle when no braid is present), as the rods surrounding the central rod, wrap around it, they behave like cantilever beams (due to fixed end), that are forced to bend, creating high stress areas at the top and bottom edges of the rods, in the direction of bending (rotation direction). However, when a constant hoop pressure is applied by the shell on the rod bundle, the surrounding rods are also forced to bend, but towards the central rod. This bending force due to the hoop pressure creates high stresses at the opposite edges of the rods in direction of the pressure applied. The higher range of stresses as observed when hoop pressure was incorporated into the model, did however not translate into a significant effect in the moment versus twist per length curves in Figure 5.9, where by incorporating hoop pressure into the model, a marginal increase (maximum of 0.4% on an average) in torsional rigidity was observed, for both diamond and regular braid topologies. The marginal increase in torsional rigidity by incorporating hoop pressure could be due to the end boundary conditions, which were replica of experimental set up, where both ends of the wires were clamped resulting in the overall effect on torsional rigidity of the wires due to hoop pressure exerted by braid shell to be minimised. 132

134 Multi-scale Modelling of Hybrid Composite Armour Wires Higher stresses on the filleted edges of shell, in contact with rods Stresses due to rotation, as rods wrap around central rod behaving like cantilever beams bending in direction of rotation Rotating end Fixed end (a) Stresses due to applied hoop pressure on the braid shell Stresses due to hoop pressure forcing the rods (that act as cantilever beams) to bend towards the central rod Rotating end Fixed end (b) Figure 5.10: Stress (von Misses in Nmm -2 ) distribution in multiscale model for 45 braid with diamond braid topology at 3 /m twist: (a) without hoop pressure, and (b) 133

135 Multi-scale Modelling of Hybrid Composite Armour Wires with hoop pressure. Note: SNEG (fraction = -1) implies stresses at face of shell in Flexural behaviour contact the rods. Three point flexure The experimental behaviour of hybrid composite wires and the behaviour from multiscale model, for different braid configurations have been shown in Figure 5.9, for a 3 point flexural set-up. As observed in Figure 5.11, a good agreement was found between experimental and multiscale model, when no hoop pressure was incorporated into the model. However, when hoop pressure is incorporated, fair agreement was observed with the experimental behaviour, with a maximum deviation of 11% for 55 braid angle with diamond braid topology because of highest hoop pressure value. The reason for higher deviations between the experimental and multiscale model behaviour could be due to the experimental test procedure followed. The test specimens are cut from very long hybrid wires and then taped at the ends for applying the boundary conditions. This could have altered the effective hoop pressure exerted by the over-braid on the rod bundles, especially at the specimen ends. This could also be the reason for a better correlation observed between the predicted (when no hoop pressure is applied) and experimental behaviour. If specimen lengths which are longer than the minimum requirement of the test standard used (which recommends a minimum extra length of 10% of span length at both the ends), the effects arising from the specimen preparation are expected to be considerably reduced. 134

136 Multi-scale Modelling of Hybrid Composite Armour Wires Figure 5.11: Experimental and FE behaviour of hybrid composite wires for 3 point flexural test 135

137 Multi-scale Modelling of Hybrid Composite Armour Wires As observed in Figure 5.11, experimentally, a marginal change in flexural behaviour was observed with change in braid angle. The minor change could be due to the dry nature of the braid. When the braid is impregnated with resin (i.e. in rigid composite form), its effect was more pronounced, and an increase in the braid angle leads to a decrease in flexural rigidity as stated in [105]. The effect of hoop pressure exerted by the braid tows on the rod bundle will not be significant when the braid is impregnated by the resin, in such as case, the braid angle will control the flexural behaviour. The effect of braid angle and braid topology was captured with the help of multiscale model which otherwise could not be observed experimentally. As expected (trend observed in [105]), an increase in braid angle led to a decrease in flexural rigidity when no hoop pressure was present. However, as hoop pressure was incorporated, the hoop pressure controlled the flexural behaviour of hybrid composite wires, such that an increase in hoop pressure that increases with increase in braid angle, led to an increase in flexural rigidity. The diamond braided structures depicted higher flexural rigidities as compared to regular braided structures, due to higher hoop pressure values (see Table 5.6). The stress distribution in hybrid composite wires, due to flexural deflection, can be observed in Figure 5.12, where the effect of hoop pressure can also be observed, at 0.25 m -1 curvature (2.5 mm deflection), for both cases: one without any hoop pressure (Figure 5.12a), and one with hoop pressure (Figure 5.12b). Similar stress distribution patterns were observed in both cases (with and without hoop pressure). The crosssection plane in contact with the support pin had the highest stress concentration on the bottom rods (at the points resting on the support pin) as the bottom-most rods were constrained in downward direction. 136

138 Multi-scale Modelling of Hybrid Composite Armour Wires Tensile and compressive stresses on the non-bonded rods Cross-section in contact with load pin (rods only) at mid-span Bottom rods are constrained in downward direction Cross-section in contact with support pin (rods only) at mid-span Stresses due to downward force exerted by the upper rods Stresses due to applied downward displacement Cross-section in contact with load pin (shell only) at mid-span Edges constrained in downward direction (a) Cross-section in contact with support pin (shell only) at mid-span 137

139 Multi-scale Modelling of Hybrid Composite Armour Wires Cross-section in contact with load pin (rods only) at mid-span Tensile and compressive stresses on the non-bonded rods Bottom rods constrained in downward direction Cross-section in contact with support pin (rods only) at mid-span Stresses due to downward force exerted by the upper rods Stresses due to applied downward displacement Stresses due to hoop pressure Cross-section in contact with load pin (shell only) at mid-span Edges constrained in downward direction Cross-section in contact with support pin (shell only) at mid-span (b) 138

140 Multi-scale Modelling of Hybrid Composite Armour Wires Figure 5.12: Stress (von Misses in Nmm -2 ) distribution in multiscale model for 45 braid with diamond braid topology at a mid-span deflection of 2.5 mm, in a 3 point flexural set-up, (a) without hoop pressure and (b) with hoop pressure. Note: SNEG (fraction = -1) implies stresses at face of shell in contact the rod For the cross-sectional plane in contact with the load pin (experimentally; at midspan), similar stress distribution patterns were observed for all rods, with higher stress concentrations at the top and bottom edges of each rod. Higher strains formed on the rods, at the top and bottom edges, resulted in tensile (bottom edge) and compressive stresses (top edge). The braid shell depicted very low stresses in comparison with the rods, primarily due to its lower stiffness (E ) 11 values in comparison to the composite rods. The higher maximum stress values in case of hoop pressure, translated into bending moment versus curvature curves in Figure Maximum deviation of nearly 2.5% was shown by 55 diamond braid containing hoop pressure, when compared with behaviour when no hoop pressure was present. The least deviation was shown by 30 regular when behaviour with hoop pressure was compared with behaviour without any hoop pressure, due to lowest hoop pressure values. Four point flexure The experimental behaviour of hybrid composite wires and the finite element model behaviour, for different braid configurations have been shown in Figure 5.13, for a four point flexure set-up. However, when the equivalent hoop pressure is incorporated, some deviation in stiffness, compared to the case with no hoop pressure, is observed between the experimental and multi-scale model behaviour, with a maximum deviation of 19.5% for 55 braid angle with diamond topology, due to highest hoop pressure value. The reason for this deviation between the experimental and predicted behaviour could be due to the experimental test procedure followed, similar to the case of three-point flexure. However, the reason for the higher deviation, compared to the predicted threepoint flexural behaviour, is because the load point in four point flexure is at half the distance compared to three-point flexure, reducing the effect of hoop pressure. This 139

141 Multi-scale Modelling of Hybrid Composite Armour Wires could also be the reason for a better correlation observed between the predicted (when no hoop pressure is applied) and experimental behaviour. As observed in Figure 5.13, a marginal change in flexural behaviour was observed with the change in braid angle and braid topology, from experimental tests conducted. However, the effect of braid angle and braid topology was captured with the help of multiscale model, in case of both: with and without hoop pressure. As expected (trend observed in [105]), an increase in braid angle led to a decrease in flexural rigidity. The effect of hoop pressure exerted by the braid tows on the rod bundle will not be significant when the braid is impregnated by the resin, in that case, the braid angle will control the flexural behaviour. The effect of braid angle and braid topology was captured with the help of multiscale model which otherwise could not be observed experimentally, just like in case of three point flexure as well. As expected (trend observed in [105]), an increase in braid angle led to a decrease in flexural rigidity when no hoop pressure was present. However, as hoop pressure was incorporated, the hoop pressure itself controlled the flexural behaviour of hybrid composite wires such that an increase in hoop pressure that increases with increase in braid angle, led to an increase in flexural rigidity. The diamond braided structures depicted higher flexural rigidities as compared to regular braided structures, due to higher hoop pressure values (see Table 5.6). The stress distribution in the finite element model, due to flexural deflection, can be observed in Figure 5.14, where the effect of hoop pressure can also be observed, at 0.18 m -1 curvature (mid span deflection of 2.5 mm), for both cases: one without any hoop pressure (Figure 5.14a), and one with hoop pressure (Figure 5.14b). The crosssection plane in contact with the support pin had highest stress concentration on the bottom rods (at the bottom most point resting on the support pin) and the shell edge, which was in contact with support pin (experimentally). This high stress concentration was a result of the upper rods exerting downward forces on the bottom-most rods, due to degree of constraint applied in downward direction applied on shell edge. For the cross-sectional plane in contact with load pin (at the half of mid-span length), stress 140

142 Multi-scale Modelling of Hybrid Composite Armour Wires concentrations were observed at the top face of the shell in contact with the load pin, and points on the upper face of the rods below the top face of the shell, in contact with load pin, in both Figure 5.14a, and Figure 5.14b. For the cross-section at the mid-span, all the rods depicted similar stress distribution pattern, due to the non-bonded nature of the rods; the pattern however, stems from higher strains formed at the top and bottom edges (maximum deflection), resulting in tensile (top edge) and compressive stresses (bottom edge). The braid shell depicted lower stresses in comparison with the rods, primarily due to its lower stiffness values (E ) 11 in comparison to composite rods, just as observed in case of three point flexure. The higher maximum stress values in case of hoop pressure, translated into bending moment versus curvature curves in Figure Maximum deviation of nearly 19% was shown by 55 diamond braid containing hoop pressure, when compared with behaviour when no hoop pressure was present. The least deviation was shown by 30 regular braid, when behaviour with hoop pressure was compared with behaviour without any hoop pressure, due to lowest hoop pressure values. 141

143 Multi-scale Modelling of Hybrid Composite Armour Wires Figure 5.13: Experimental and FE behaviour of hybrid composite wires for 4 point flexural test 142

144 Multi-scale Modelling of Hybrid Composite Armour Wires Stresses due to load pin Cross-section at mid-span (rods only) Bottom rods constrained in downward direction Cross-section in contact with support pin (rods only) Stresses due to downward force exerted by the upper rods Contact Stresses due to load pin Cross-section at mid-span (shell only) Edges constrained in downward direction Cross-section in contact with support pin (shell only) (a) 143

145 Multi-scale Modelling of Hybrid Composite Armour Wires Stresses due to load pin Cross-section at mid-span (rods only) Bottom rods constrained in downward direction Cross-section in contact with support pin (rods only) Stresses due to downward force exerted by the upper rods Contact Stresses due to load pin Stresses due to hoop pressure Cross-section at mid-span (shell only) (b) Cross-section in contact with support pin (shell only) 144

146 Multi-scale Modelling of Hybrid Composite Armour Wires Figure 5.14: Stress (von Misses in Nmm -2 ) distribution in multiscale model for 45 braid with diamond braid at a mid-span deflection of ~2.5 mm, in a 4 point flexural set-up: (a) without hoop pressure, and (b) with hoop pressure. Note: SNEG (fraction = -1) implies stresses at face of shell in contact the rods Summary Using the multi-scale model approach, the flexural behaviour of hybrid wires is found to be controlled primarily by the composite rods and hoop pressure value, whilst in torsion by the composite rods and shear stiffness (G12) of braid. As discussed in Chapter 4, experimentally, the effect of braid angle and braid topology on the flexural response of hybrid wires, is not found to be very significant and the trends observed remained inconclusive. The multi-scale model in contrast is capable of predicting flexural behaviour of hybrid composite wires that could not be observed experimentally. In the absence of hoop pressure, a decrease in flexural rigidity with an increase in braid angle (similar trend observed when braid is impregnated with resin) is observed, since 30 braid angle has higher axial modulus. The multi-scale model depicted lower flexural rigidities for diamond braid topology due to lower crimp values, in comparison with the regular braid topology, when no hoop pressure is incorporated. A converse trend is observed when hoop pressure is present, where an increase in braid angle leads to an increase in flexural rigidity, since the hoop pressure increases with increase in the braid angle. Higher flexural rigidities were also observed for diamond braid topologies in comparison with regular braid topology, again due to higher hoop pressure values. The effect of hoop pressure within same type of braid angle and topology was found to be again quite significant, with maximum deviation in case of 55 braid angle, due to highest hoop pressure values. If specimens with longer extra length at both sides of span were tested, a much closer correlation between experimental and multi-scale model could have been obtained, when hoop pressure was incorporated. 145

147 Multi-scale Modelling of Hybrid Composite Armour Wires In case of torsion, the multiscale model predicted a decrease in torsional rigidity with an increase in braid angle, which was in part agreement with experimental results, where maximum torsional rigidity was found for 45 braid followed by 30 and 55 braid angle, due to sensitivity of the model towards crimp (increases with increase in braid angle). The effect of braid topology was also found to be quite significant both experimentally and through multi-scale model, with higher torsional rigidity in case of regular braids. The effect of hoop pressure on the torsional response of hybrid wires was found to be negligible. Although the multi-scale model involves several assumptions, it still is successful in predicting elastic behaviour closely in comparison with the experimental behaviour. The multi-scale model helps to provide an approximate solution for mechanical behaviour of hybrid composite wires, and could possibly be used for similar structures. 146

148 Parametric Studies Using Multiscale Model Parametric Studies Using Multiscale Model T he multiscale model approach used for computation modelling of hybrid composite wires has been validated in the previous chapter for torsion and flexure mode of deformation. Although the model involves several assumptions, it still is successful in predicting elastic behaviour closely in comparison with the experimental behaviour. The multiscale model has been further used in this section to conduct a series of parametric studies, to help determine flexural and torsional rigidities obtained when different physical, structural, and material properties of composite rods and braid are used to produce hybrid composite wires Introduction The multiscale model approach used for hybrid composite wires, as stated above has been validated in the previous chapter and used here to understand the effect of friction (physical property) between different non-bonded components (composite rods and braid) of hybrid composite wires and the effect of using different model lengths (structural change). A material parametric study has also been conducted, where different combinations of material systems (for composite rods and braid) have been compared with the original material system (Dyneema braid sleeve and carbon/vinyl ester resin composite rods) used in the hybrid composite wire studied in this thesis Effect of friction The multiscale model has been used in this section to help determine the effect of coefficient of friction between the composite rods (µr), and the coefficient of friction between shell and the composite rods (µs), in case of both flexure (only 4 point flexure used) and torsion. Range of coefficients of friction values were chosen for both µr and µs, between minimum (frictionless) and maximum (equal to 1) values. The effect of friction has been shown in Figure 6.1, for only one of the braid configurations (45 147

149 Parametric Studies Using Multiscale Model braid with diamond braid topology), where hoop pressure has been incorporated, since in the absence of hoop pressure, the effect of friction was observed to be negligible in case of flexural and no effect was observed in case of torsion. The coefficient of friction between two surfaces is the ratio of the normal force and resultant force. If there is no normal force, which happens when no hoop is pressure, there will be no effect of friction. The reason for some, but negligible effect of friction in case of flexure is due to the inter-rod and rod-shell sliding during very high flexural deflections (> 70 mm). The different flexural and torsional rigidities obtained have been compared with the rigidities obtained from original coefficients of friction values, close to experimental (µr = 0.49, µs =0.06), used in the multi-scale model. Figure 6.1: Effect of coefficient of friction in hybrid composite wires using multiscale model 148

150 Parametric Studies Using Multiscale Model As observed in Figure 6.1, the lowest torsional and flexural rigidities were observed when there was no friction between the non-bonded components (µs = µr = 0) in the multi-scale model whereas, the highest torsional and flexural rigidities were observed in case of maximum coefficient of friction (µs = µr = 1). This trend is expected, since maximum coefficient of friction values will impart maximum frictional force between the components in the hybrid wires and vice-versa for minimum coefficient of friction values. The effect of friction in case of torsion was found to be marginal, with an increase in torsional rigidity of only 2.5% as the values of coefficient of friction were increased from minimum to maximum. On the other hand, the effect of friction in case of flexure was found to be more pronounced, where an increase in flexural rigidity of 31% was observed, as the values of coefficient of friction were increased from minimum to maximum. The effect of µs was found to be more pronounced in case of flexure, with an increase of nearly 12.1% as value of µs was increased from to While in case of torsion this increase was about 1.4%. Similarly the effect of µr was also found to be more pronounced for flexural, where an increase of 7% was observed in case of flexure and 1.7% in case of torsion, as the value of µr was increased from 0.49 to the maximum value of Effect of model length The multiscale model has been used in this section for a specific hybrid wire configuration (45 braid with diamond braid topology with hoop pressure), to determine the effect of model length, which can also be rephrased as the effect of gauge length in case of torsion, and effect of span length in case of flexure. It was initially expected that the elastic properties of the model will remain independent of the model length, however a contrary trend was observed, which has been shown in Figure 6.2, due to anisotropic nature of different components in the wire. 149

151 Parametric Studies Using Multiscale Model The knowledge of the effect of length is pivotal, to determine what the optimum length to thickness ratio for mechanical testing of the hybrid composite wires is. Another reason to determine an optimum length to thickness ratio is that the hybrid wires consist of several non-bonded components, and as there are no specific standards for testing such a structure, this information can be useful. As the gauge length was increased, a decrease in torsional rigidity was observed. The drop in torsional rigidity of nearly 7.4% was observed initially, as the length increased from 100 mm to 200 mm, followed by a lower drop of 2.1% as the length was increased from 200 mm to 300 mm. Beyond 300 mm a saturation was achieved, where a drop in torsional rigidity of only 0.5% was observed as gauge length was increased from 300 mm to 400 mm and a further lower drop of only 0.1% as the length was increased to 500 mm. Figure 6.2: Effect of length in hybrid composite wires using multiscale model In case of flexure, an inverse trend was observed where an increase in model length (span length) led to an increase in flexural rigidity. As the model length was doubled from 100 mm to 200 mm, a big increase of 22.7% was observed, and by further increasing the span length to 300 mm a lower increase in flexural rigidity of 5.1% was 150

152 Parametric Studies Using Multiscale Model observed. However, this increase started to saturate beyond 300 mm, with flexural rigidity decreasing at much slower rate. The reason for this inverse trend is because, in case of lower length to thickness ratio the behaviour is predominantly governed by shear forces alone rather than by both axial forces (that control flexural rigidity in longer lengths). The effect of span length has been studied in [163] where similar behaviour was observed as in case of hybrid wires, with shortest span depicting significantly lower flexural stiffness, than higher span lengths. Hence, higher length to thickness ratios (> 38:1) should be used for flexure and torsion testing of hybrid composite wires, and for their computational modelling Different combinations of material systems This section focusses on the parametric study of hybrid composite wires by varying material systems for braid fibres and composite rods. In order to determine the effect of changing material systems in case of composite rods, two types of composite rods: carbon/vinyl-ester (already incorporated in original configuration of hybrid composite wires) and glass/vinyl-ester were compared. The effect of changing material type for resin has not been carried out in this thesis. The elastic properties of glass rods were determined using analytical equations from literature (Eqs. (4.6), (4.7), (5.1) to (5.8)). The elastic properties of carbon & glass fibres, and vinyl-ester resin has been reported in Table 6.1, and the elastic properties of carbon/vinyl-ester & glass/vinyl-ester composite have been reported in Table 6.2. The coefficient of friction between glass/vinyl-ester composite rods (µr) was assumed to be same as coefficient of friction between carbon/vinyl-ester rods (µr = 0.49), since the frictional behaviour of pultruded composite rods will be controlled by the matrix rich layer at their circumference. To determine the effect of changing material systems for braid shell, three fibres for the same braid configuration (45 braid, with diamond braid topology and hoop pressure) have been compared: carbon, glass (E-glass) and Dyneema (or UHMW-PE fibres, already incorporated in the original configuration of hybrid composite wires). The process of determining the elastic properties of the braid sleeve with carbon and glass fibres was same as quantification of elastic properties of Dyneema sleeves as 151

153 Parametric Studies Using Multiscale Model described in Chapter 5 (Pg. 114). The tow geometry, braid crimp, volume of braid tows, and the total volume of braid unit cell for carbon and glass braids, were assumed to same as Dyneema braid sleeve. Table 6.1: Properties of different fibres and matrix systems obtained from literature [with references] Type E11 G12 ν12 (GPa) (GPa) Glass fibre 77.4 [164] 30.4 [164] 0.22 [164] Carbon fibres 230 [136] 24 [136] 0.27 [136] Dyneema fibres 116 [128] 0.95 [129] 0.29 [149] Vinyl-ester matrix 2.9 [137] 1.17 [138] 0.35 [138] HD-PE matrix 0.70 [150] 0.25 [151] 0.40 [152] Table 6.2: Properties of different composite rods Type of rods E11 (GPa) E22 (GPa) E33 (GPa) G12 (GPa) G13 (GPa) G23 (GPa) ν12 ν13 ν23 Carbon ± 1.65* ± 0.10* Glass * determined experimentally The value of the coefficient of friction between carbon tow and composite rod was found to be 0.22 ± 0.002, whilst the coefficient of friction between glass fibre tows and composite was found to be 0.32 ± The methodology for quantification of value of coefficient of friction between fibres and composite rods has been described in detail in Chapter 3 (Pg. 78), using Capstan s equation. The values of coefficient of friction between fibre tows and composite rod obtained were used as coefficient of friction between braid shell and composite rods (µs). The elastic properties of glass and carbon fibres and tows, and HD-PE resin matrix, used to quantify the elastic properties of braid shell have been reported in Table 6.1. The elastic properties of tows 152

154 Parametric Studies Using Multiscale Model calculated using (Eqs. (4.6), (4.7), (5.1) to (5.8)), have been reported in Table 6.3, where carbon fibre tow depicts highest modulus both in principle material direction (E11, E22, E33 ) and shear directions (G12, G13, and G23). The highest modulus values also translated into stiffest response in case of braid shell, in Table 6.4. The elastic properties of Dyneema fibre tows as observed in Table 6.3, showed higher axial and transverse modulus values, in comparison to glass fibre tows however, depicted lower in-plane shear modulus, primarily due to the lowest in-plane shear modulus among three fibres tows. Table 6.3: Properties of different braid tows Type of E11 E22 E33 G12 G13 G23 ν12 ν13 ν23 tow (GPa) (GPa) (GPa) (GPa) (GPa) (GPa) Dyneema Glass Carbon Table 6.4: Properties of different braid shell Type of shell E 11 (GPa) E 22 (GPa) E 33 (GPa) G 12 (GPa) G 13 (GPa) G 23 (GPa) ν 12 ν 13 ν 23 Dyneema Glass Carbon However, higher axial modulus of Dyneema fibre tows in comparison with glass fibre tows, did not result in higher axial modulus of the braid shell (E ). 11 The reason for this trend is that the analytical model used to calculate the elastic properties of the braid shell, uses combination of both axial, transverse, through thickness, and shear properties, of a fibre tow to determine a specific engineering constant. However, if the shell properties of 30 braid angle are compared for all three types of braid shell 153

155 Parametric Studies Using Multiscale Model (carbon, glass, & Dyneema), the E 11 values for Dyneema braid shell will be considerably higher than glass braid shell. Figure 6.3: Torsional rigidities of hybrid composite material with different combination of material system using multi-scale model The torsional rigidities of hybrid composite wires using different combinations of material systems for composite rods and braid shell have been shown in Figure 6.3. The highest torsional rigidity was shown when glass composite rods were used with carbon over-braid sleeve. This was 70% higher than the combination of material system used to produce hybrid composite wires studied in this thesis, which on the contrary, showed the lowest torsional rigidity. The highest torsional rigidity for hybrid composite wire with glass composite rods and carbon over-braid sleeve arises from highest in-plane shear modulus predicted (see Table 6.2 & Table 6.4) for both rods and shell. The second highest torsional rigidity was depicted when a combination of glass composite rods and glass over-braid sleeve were used. 154

156 Parametric Studies Using Multiscale Model Figure 6.4: Flexural rigidities of hybrid composite material with different combination of material system using multi-scale model A completely different trend observed for flexural rigidities of hybrid composite wires using different material systems for composite rods and over-braid sleeve (shown in Figure 6.4). The highest flexural rigidity as shown in Figure 6.4, was depicted by a combination of carbon composite rods and carbon braid sleeve. This was 31% higher than the combination of material system of carbon composite rods with Dyneema over-braid sleeve, used to produce hybrid composite wires studied in this thesis, which unlike in case of torsion did not show lowest flexural rigidity. The highest flexural rigidity when carbon composite rods are used with carbon over-braid sleeve is due to the highest predicted axial stiffness (which primarily controls the flexural rigidity of a structure) for both composite rods and over-braid sleeve. The lowest flexural rigidity was shown by a combination of glass composite rods and glass over-braid sleeve, although the axial modulus for over-braid sleeve was higher than Dyneema over-braid sleeve. This is due to lowest axial modulus value for glass composite rods, since in the composite rods control the flexural rigidity of hybrid composite wires. 155

157 Parametric Studies Using Multiscale Model 6.5. Summary Using multi-scale modelling technique, series of parametric studies were conducted in this chapter. The parametric studies conducted, helped in understand the role of composite rods and braid shell, and the material properties associated in determining the torsional and flexural rigidities of hybrid composite wires. The coefficient of friction between the braid shell and composite rods, and between the composite rods is more pronounced in case of flexure than torsion. As the coefficient of friction was increased between the components in finite element model, the flexural and torsional rigidities also increased. The effect of model length was found to be significant for both torsion and flexure, with an inverse trend observed, as the model length was increased; the torsional rigidity decrease in model length, whilst the flexural rigidity increased with an increase in model length. A span to thickness ratio (> 38:1) should be used to obtain accurate flexural and torsional rigidities of hybrid composite wires. The parametric study conducted by varying the material systems in hybrid composite wires, showed highest torsional rigidity exhibited by glass composite rods with carbon over-braid sleeves. The highest flexural rigidity was depicted by a combination of carbon composite rods and carbon over-braid sleeve. The actual hybrid composite wire studied in the thesis that consisted of carbon composite rods and Dyneema over-braid sleeve shower lower rigidities in both flexure and torsion. 156

158 Conclusions and Directions for Future Research Conclusions and Directions for Future Research I n the study presented in this thesis, an alternative to traditional metallic tensile armour wires was introduced, in form of flexible hybrid composite wire, produced using pultrusion and braiding process. A detail manufacturing study was conducted for hybrid composite wires and their mechanical behaviour was examined through experimentation and computation modelling. In this chapter the conclusions from the study conducted, and the directions for future research have been presented Manufacturing study The hybrid composite wires comprises of seven unidirectional pultruded composite rods with carbon fibres and vinyl-ester resin matrix, bundled in form of hexagonal closed pack. The pack was held together by an over-braid sleeve with Dyneema fibres. Different configurations of hybrid composite wires were studied under flexure and torsion by varying different structural parameters of constituents of these wires in form of: diameter of rods (Ф 2 mm and Ф 4 mm), braid angle (30, 45, and 55 ), and braid topology (diamond and regular). Full braid coverage was used for all configurations of hybrid composite wires studied, in order to minimise the effect friction arising due to wire to wire interaction in an actual riser environment, since the braid fibres (Dyneema) depicts 90% lower coefficient of friction as compared to composite rod to rod friction coefficient. Out of two maypole braiding machines (24 and 48 carrier) used to produce hybrid composite wires, commercially only one type of braiding machine can be used to produce these wires. In this context, the 24 carrier braiding machine could be used as it is capable of over-braiding both types of bundled rods (one with Ф 2 mm rods and other with Ф 4 mm rods). Moreover it can over-braid broad range bundle thicknesses, in comparison with 48 carrier braiding machines that cannot braid hybrid composite wires with individual rod diameter equal and smaller than 2 mm (with required criteria 157

159 Conclusions and Directions for Future Research mentioned on Page 63), and are also comparatively double in the size. An optimum braid tension needs to be maintained during the braiding process, since a very low braid tension will not be able to hold the bundled rods effectively, and very high tension can exert very high hoop pressure on the rod bundle not allowing the inter-rod slippage, increasing the flexural and torsional rigidity. Non-destructive structural health monitoring of flexible risers is essential especially when operating in deeper depths using optical fibres and embedded sensors, and is now extensively being used in flexible risers. With help of manufacturing processes involved in producing hybrid composite wires, these optical fibres and sensors can be easily incorporated during pultrusion and braiding processes, helping in structural health monitoring of every component of every hybrid composite wire in the tensile armour Mechanical characterisation The flexural and torsional behaviour of hybrid composite wires was investigated. The effect of the rod diameter used in the bundle, on flexural and torsional rigidity proved to have the most significant effect, due to an increase second area moment (flexure) of inertia or polar area moment (torsion) of inertia as the individual rod diameter is increased, increasing the flexural and torsional rigidities significantly. The effect of other parameters such as braid angle and braid topology, on torsional and flexural rigidities, was also found to be more pronounced in case of torsion than flexure, where the trends (in the elastic region) observed remained inconclusive. In torsion, out of three braid angles (30, 45, and 55 ) investigated, 45 braid angle exhibited highest torsional rigidity followed by 30 and 55 braid angles (similar trend observed in literature for similar structures). The effect of braid topology was also observed, with regular braid topology depicting higher torsional rigidity as compared to diamond braid topology (due to lower crimp values). The effect of braid angle and braid topology in flexure was found to be more pronounced in the inelastic region, where 30 braid angles in both diamond and regular braid topologies underwent packing deformation. The effect of hexagonal packing of composite rods was also observed in case of flexure, where the single rods underwent pre-mature fracture in 158

160 Conclusions and Directions for Future Research comparison with hybrid composite rods that did not fail upto maximum tested limit. This observation helped to infer that the failure of the individual rods in hybrid composite wires gets delayed due to the inter-rod slippages, with the over-braid helping in absorbing effects from high flexural loads. Due to the same reasons, the hybrid composite rods also showed inelastic response in comparison with single rods that only showed elastic behaviour. The effect of end boundary condition on the flexural behaviour of hybrid composite wire was also carried out in this thesis, where the ends of the wires were bonded instead of being taped, to get an idea of how these wires will behave near the end fittings of the riser. It was found that the flexural rigidity for specimens with bonded ends was twice as compared the specimens with taped edges. On comparison of flexural and torsional rigidities of hybrid composite tensile armour wires with traditionally used wires it was found: The hybrid composite rods with Ф 4 mm rods, depicted significantly higher (8 times) flexural rigidities in comparison with traditionally used metallic wires, whilst the wires with Ф 2 mm rods depicted comparatively lower (3.5 times) flexural rigidities. If the torsional rigidities were compared, hybrid composite rods with Ф 4 mm rods, depicted significantly lower (133 times) torsional rigidities in comparison with traditionally used metallic wires, whilst the wires with Ф 2 mm rods depicted comparatively exceptionally lower (1660 times) torsional rigidities. It is also essential to use higher braid angles in hybrid composite wires, ideally with diamond braid topology, to improve the in-through thickness compressive strengths of the hybrid composite wires. The trends clearly prove the flexural and torsional compliance of hybrid composite wires. The hybrid composite rods with Ф 2 mm rods, that have approximately thrice the thickness of metallic armour wires, depicts significantly lower rigidities, and could also help in reducing the additional cross-winding step (to increase annulus thickness of riser), helping in lowering production time significantly. 159

161 Conclusions and Directions for Future Research 7.3. Multi-scale model and parametric studies A multi-scale finite element model for the hybrid composite wires, using a combined analytical and computational approach was presented in this thesis. This approach provided a simpler and computationally less expensive solution to modelling an otherwise complex structure of the hybrid composite wires. The multi-scale modelling helped in understanding the role of the varying structural parameters of over-braid sleeve on the torsional and flexural behaviour (elastic) of hybrid composite wires. The model was validated for different configurations of hybrid composite wires, where a good agreement was found between experimental and multi-scale model behaviour. The effect of braid angle, braid topology and hoop pressure exerted by the braid shell on composite rods that were not observed clearly experimentally, could be observed using multi-scale model. In flexure, the absence of hoop pressure an increase in braid angle lead to a corresponding decrease in flexural rigidity. The diamond braid topology depicted lower flexural rigidities as compared to regular braid topology due to higher crimp values. While in presence of hoop pressure, an increase in braid angle led to an increase in flexural rigidities due to an increase in hoop pressure values, with diamond braid topology showing higher flexural rigidities. The higher grip in case of 45 and 55 braids confirms higher hoop pressure exerted by them, in comparison with 30 braids that underwent packing deformations during experimental tests conducted. In case of torsion, the multi-scale model predicted a decrease in torsional rigidity with an increase in braid angle, due to the sensitivity of the model towards braid crimp, which increases with an increase in braid angle. The model was however, successful in predicting higher torsional rigidities in case of regular braid structures. The effect of hoop pressure was found to be negligible, possibly due to the end boundary conditions and kinematic coupling constraining both the ends (mimicking experimental behaviour where the ends were clamped). The multi-scale model was used to understand the effect on torsional and flexural behaviour of hybrid composite wires by varying frictional properties between different components and the effect of varying span and gauge lengths (model length). As 160

162 Conclusions and Directions for Future Research expected the increase in coefficient of friction led to an increase in rigidities for both: friction between braid shell and rods, and between rods had effects; with the effect of friction more pronounced in case of flexure. The effect of model length was also a significant finding where converse trends were observed. An increase in model length led to a decrease in torsional rigidity and an increase in flexural rigidity. Through parametric study conducted, a span to thickness ratio of more than 38:1 has been recommended. The effect of using different combinations of material systems in hybrid composite wires was also conducted. Three braid sleeves (with carbon, glass, and Dyneema) were used in combination of two composite rods (carbon and glass). The highest torsional rigidity was shown by wires with carbon sleeve and glass rods, and highest flexural rigidity was shown by wires with carbon sleeve and carbon rods. The hybrid composite wires (Dyneema sleeves and carbon rods) showed lowest torsional rigidity among the combinations studied, whilst fell in between the range of highest and lowest rigidities in case of flexure. If the cost of production is a concern, glass fibre rods and glass braids can be used to produce hybrid composite wires, since glass fibres are comparatively cheaper than carbon fibres, but the resultant structure as proved using multi-scale model can have higher torsional rigidity and lower flexural rigidity. The multiscale model proved to be a very useful approach that can be used to conduct different parametric studies in order to understand the behaviour of hybrid composite wires. However, the multiscale modelling approach cannot be applied to understand the behaviour of the hybrid wires at higher strains, when the braid tows begin to shear, which can change the associated braid angle. The model can successfully be used to predict elastic properties of hybrid wires at lower strain values, when the shearing of braid tows is negligible. However, by determining the rate of change of braid angle with increasing strain, additional algorithms can be fed into the finite element package to apply the model even to higher strains levels. The multi-scale model helps in providing an approximate solution of the elastic properties of braid shell and could be applied for similar structures. 161

163 Conclusions and Directions for Future Research 7.4. Recommendations for future work In this thesis, a promising alternative to metallic tensile armour wires as hybrid composite wire was proposed, investigated, and a finite element model to help understand the properties of these wires further was presented. However, there are several aspects of the hybrid composite wires that could be investigated to further highlight advantages or limitations of these tensile armour wires for commercial application: The behaviour of hybrid composite wires in actual riser environment can be studied. The hybrid composite wires can be wound on to a pipe with similar diameter as the flexible riser, and can be subjected to flexure, to examine the curvature of failure of these wires. The effect of lay angle on the performance of the tensile armours containing the hybrid composite wires can also be investigated. A similar test can be conducted for flexural fatigue. There are already testing standard for testing of radial and lateral buckling of metallic tensile armours by American Institute of Petroleum [17] and ISO [165], which could be also be used to examine the behaviour of hybrid composite wires under these test conditions. The multi-scale model used for hybrid composite wires, can be used to extrapolate the elastic properties of these wires in all principle directions, following that the wire structure itself can be modelled as an orthotropic solid hexagon (with filled edges). The hybrid composite wire can be modelled around the curvature of the pipe, and series of studies can be carried out using finite element analysis. It will however be essential to incorporate the tensile and shear strengths of composite rods in the hybrid composite wires in the model. The ageing aspect of the hybrid composite wires can also be investigated. The effect of ageing to understand the effect of salinity of water on the mechanical properties of these wires needs to be carried out, and could potentially help in boosting its commercialisation. 162

164 Bibliography Bibliography 1. Pertrobras. Petrobras receives highest award in global oil industry (highest depth acheived for flexible riser) [cited 2016; Available from: 2. Boschee, P., Best Practices for flexible pipe intergrity, in Oil and Gas Facilities Kalman, M. and J. Belcher, Flexible Risers with Composite Armor for Deep Water Oil and Gas Production. Composite Materials for Offshore Operations, 1999: p Do, A.T. and A. Lambert, Qualification of Unbonded Dynamic Flexible Riser With Carbon Fibre Composite Armors. 2012, Offshore Technology Conference. 5. Do, A.T., G. Bernard, and D. Hanonge, Carbon Fiber Armors Applied to Presalt Flexible Pipe Developments, in Offshore Technology Conference. 2013: Houston, Texas, USA. 6. Jha, V., et al., Optimized Hybrid Composite Flexible Pipe For Ultra- Deepwater Application, in 34th International Conference on Ocean, Offshore and Arctic Engineering. 2015, ASME: St. John's, Newfoundland, Canada. 7. N. Ismail, R.N., and M. Kanarellis, Design consideration for selection of flexible riser configuration. Offshore and Arctic Operations, Dingenen, J.L.J.v., High performance dyneema fibres in composites. Materials & Design, (2): p Moore, F., Materials for flexible riser systems: problems and solutions. Engineering Structures, : p Sævik, S., Theoretical and experimental studies of stresses in flexible pipes. Computers & Structures, (23-24): p Qiang, B. and B. Yong, Subsea Pipeline Design, Analysis, and Installation. 1st ed. 2014, Oxford: Elsevier. 12. Fergestad, D. and S.A. Løtveit, Handbook on Design and Operation of Flexible Pipes. 2014: MARINTEK / NTNU / 4Subsea. 13. Seaflex, Failure modes, inspection, testing and monitoring. 2007, PSA - NORWAY Flexible Pipes: Norway. 14. Seguin, B.R. and R.A. Maloberti, Flexible pipe for riser in off-shore oil production. 2000, US Patent. 15. Farnes, K.-A., et al., Carcass failures in multilayer PVDF risers in 32nd International Conference on Ocean, Offshore and Arctic Engineering. 2013, ASME: Nantes, France. 163

165 Bibliography 16. Berge, S., et al., Handbook on design and operation of flexible pipes Institute, A.P., Practice For Flexible Pipe. AN-SI/API Recommended Practice 17B de Sousa, J.R.M., et al., On the response of flexible risers to loads imposed by hydraulic collars. Applied Ocean Research, (3): p Hansen, R., et al., Carcass tearing in flexible pipes in 34th International Conference on Ocean, Offshore and Arctic Engineering. 2015, ASME: St. John's, Canada. 20. Lange, H., et al., Material selection in the offshore industry Ebrahimi, A., S. Kenny, and A. Hussein, Parameters Influencing Birdcaging Mechanism for Subsea Flexible Pipe, in Proceedings of the Twenty-fifth (2015) International Ocean and Polar Engineering Conference. 2015, International Society of Offshore and Polar Engineers: Hawaii. p PSA-Norway, Un-bonded Flexible Risers Recent Field Experience and Actions for Increased Robustness. 2013: Nesbru. 23. Singh, R., Chapter 6 - Classification of Steels, in Applied Welding Engineering (Second Edition), R. Singh, Editor. 2016, Butterworth-Heinemann. p Johnson, V.H., 7 - Plain Carbon and Alloy Steels, in Manufacturing Processes, V.H. Johnson, Editor. 1984, Macmillan/McGraw-Hill. p Singh, A., Part D - Chapter 21 in Machine Drawing, A. Singh, Editor. 2008, McGraw-Hill. p Tong, W., Chapter 3 - Shaft Design, in Mechanical Design of Electric Motors, W. Tong, Editor. 2014, CRC Press. p Roberts, W.L., History of Hot Rolling, in Hot Rolling of Steel, L.W. Roberts, Editor. 1978, Marcel Dekker. 28. Yamada, Y. and T. Kuwabara, Chapter 2 - Metallic Material for Springs, in Materials for Springs. 2007, Springer Berlin Heidelberg. p Qiang, B. and B. Yong, Subsea Pipelines and Risers. 2005, London: Elsevier. 30. Institute, A.P., Practice For Flexible Pipe. AN-SI/API Recommended Practice 17B. 2002, American Petroleum Institute. 31. Petroleum, A.I., Specification for Un-bonded Flexible Pipe : API 17J Guo, B., et al., Chapter 10 - Introduction to Flexible Pipelines, in Offshore Pipelines (Second Edition), B.G.S.G.R. Lin, Editor. 2014, Gulf Professional Publishing: Boston. p Executive, H.a.S., Guidelines for integrity monitoring of Unbonded flexible pipe - OTO , Heath and Safety Exectutive. 34. Xu, K. and X.W. Xu, Finite element analysis of mechanical properties of 3D five-directional braided composites. Materials Science and Engineering: A, (1-2): p

166 Bibliography 35. Doynov, K. Improving standards and technology towards achieving robust design and safe operations of flexible risers. in PSA Flexible Risers Seminar Stavangar. 36. Désamais, N., et al., Use of High Strength Steel Wires For Flexible Pipe In Low Sour Service Conditions: Impact On Deep Water Applications, in The Seventeenth International Offshore and Polar Engineering Conference. 2007, International Society of Offshore and Polar Engineers: Lisbon, Portugal. p Reuben, R.L., Chapter 7 - Case Studies and Applications, in Materials in Marine Technology. 1994, Springer London. p Krauss, G. Steels: processing, structure, and performance: Ohio. in ASM International Clarke, T., et al., Monitoring the structural integrity of a flexible riser during a full-scale fatigue test. Engineering Structures, (4): p Pipa, D., et al., Flexible Riser Monitoring Using Hybrid Magnetic/Optical Strain Gage Techniques through RLS Adaptive Filtering. EURASIP Journal on Advances in Signal Processing, Marinho, M.G., et al., New Techniques for Integrity Management of Flexible Riser-End Fitting Connection. ASME, June : p Marinho, M.G., J.M. Santos, and R.O. Carneval. Integrity assessment and repair, techniques of flexible risers. in 25th ASTM international conference on offshore mechanics and arctic engineering McCarthy, J.C. and D.J. Buttle, Non-Invasive Magnetic Inspection of Flexible Riser Structural Integrity. 2009, Offshore Technology Conference. 44. Sævik, S. and M.J. Thorsen, Techniques for Predicting Tensile Armour Buckling and Fatigue in Deep Water Flexible Pipes. 31st International Conference on Ocean, Offshore and Arctic Engineering, 2012: p Loper, C., et al. Behavior of Tensile Wires in Unbonded Flexible Pipe Under Compression and Design Optimization for Prevention. in 25th International Conference on Offshore Mechanics and Arctic Engineering American Society of Mechanical Engineers. 46. Bectarte, F. and A. Coutarel. Instability of Tensile Armour Layers of Flexible Pipes Under External Pressure. in 23rd International Conference on Offshore Mechanics and Arctic Engineering Vancouver: American Science of Mechanical Engineers. 47. Braga, M.P. and P. Kaleff. Flexible Pipe Sensitivity to Birdcaging and Armor Wire Lateral Buckling. in 23rd International Conference on Offshore Mechanics and Arctic Engineering Vancouver: American Society of Mechanical Engineers. 48. Østergaard, N.H., A. Lyckegaard, and J.H. Andreasen. On Lateral Buckling Failure of Armour Wires in Flexible Pipes. in 30th International Conference on Ocean, Offshore and Arctic Engineering Rotterdam: American Science Of Mechanical Engineers. 165

167 Bibliography 49. Østergaard, N., A. Lyckegaard, and J.H. Andreasen, Imperfection analysis of flexible pipe armor wires in compression and bending. Applied Ocean Research, : p Zhou, C., et al., Effect of lay angle of anti-buckling tape on lateral buckling behavior of tensile armors. 34th International Conference on Ocean, Offshore and Arctic Engineering, (A). 51. Shioya, M. and T. Kikutani, Chapter 7 - Synthetic Textile Fibres: Non-polymer Fibres, in Textiles and Fashion, R. Sinclair, Editor. 2015, Woodhead Publishing. p Jeon, Y.-P., et al., Chapter Carbon Fibers, in Handbook of Advanced Ceramics, S. Somiya, Editor. 2013, Academic Press: Oxford. p Edie, D.D. and J.J. McHugh, Chapter 4 - High performance carbon fibers, in Carbon materials for advanced technologies. 1999, Elsevier Ltd. p Bahl, O.P., et al., Chapter 1 - Structure of Carbon fibres, in Carbon fibers, J.- B. Donnet, et al., Editors. 1998, CRC Press. p Lavin, J.G., Fracture of carbon fibers. Fiber Fracture, 2002: p Greenwood, J.H. and P.G. Rose, Compressive behaviour of Kevlar 49 fibres and composites. Journal of Materials Science, (11): p Chin, J., et al., Effect of artificial perspiration and cleaning chemicals on the mechanical and chemical properties of ballistic materials. Journal of Applied Polymer Science, (1): p Horrocks, A. and S. Anand, Handbook of Technical Textiles. 2000, Cambridge: Woodhead Publishing Limited. 59. Berger, L., H.H. Kausch, and C.J.G. Plummer, Structure and deformation mechanisms in UHMWPE-fibres. Polymer, (19): p Dangsheng, X., Friction and wear properties of UHMWPE composites reinforced with carbon fiber. Materials Letters, (2-3): p Tuttle, M.E., Chatpter 1: Introduction, in Structural Analysis of Polymer Composites. 2004, Marcel Dekker, Inc. 62. Pascault, J.P., et al., Chapter 1: Introduction, in Thermosetting Polymers. 2002, Marcel Dekker. 63. Pıhtılı, H. and N. Tosun, Investigation of the wear behaviour of a glass-fibrereinforced composite and plain polyester resin. Composites Science and Technology, (3): p Pereira, C.M.C. and M.S.S. Martins, Chapter 17 - Flame Retardancy of Fiber- Reinforced Polymer Composites Based on Nanoclays and Carbon Nanotubes, in Polymer Green Flame Retardants, C.D. Papaspyrides and P. Kiliaris, Editors. 2014, Elsevier: Amsterdam. p Institute, C., Chapter 2 : Introduction to Composite Materials, in Introduction to Composites p

168 Bibliography 66. Blankenship, L.T. and M.N. White. Vinyl ester resins: versatile resins for composites. in Proceedings of the 34th International SAMPE Symposium Clemitson, I.R., Castable polyurethane elastomers. 2008, London: CRC Press. 68. Morgan, P., Carbon Fibers and Their Composites. 2005: CRC Press. 69. Nando, G.B. and B.R. Gupta, Chapter 4 - Short fibre-thermoplastic elastomer composites in Short Fibre-Polymer Composites, S.K. De and J.R. White, Editors p Shaw-Stewart, D. and J.E. Sumerak, Chapter 2 : The Pultrusion Process, in Pultrusion for Engineers, T.F. Starr, Editor. 2000, Woodhead Publication. 71. Sumerak, J.E., The Pultrusion Process for Continuos Automated Manufacture of Engineered Composite Profiles, in Composites Engineering Handbook, P.K. Mallick, Editor. 1997, Marcel Dekker, Inc. 72. Kimpara, I., Use of advanced composite materials in marine vehicles. Marine Structures, (2): p Chalmers, D.W., The Potential for the use of composite materials in marine structures. Marine Structures, (2 5): p Gibson, A.G., The cost effective use of fibre reinforced composites offshore Ahlstone, A., Light weight marine riser pipe, US A,. 1973, Vetco Offshore Ind Inc. 76. Pierce, R.H., Composite marine riser system, US A,, U.S. Patent, Editor. 1987, Vecto offshore Inc. 77. Lotveit, S.A. and H.L. Ward, Fibre Reinforced Flexible Pipe Material Selection And Design Methods, in International Society of Offshore and Polar Engineers. 1991: Edinburgh. 78. Coflexip, CLAROM internal report. 1993, Bureau Veritas: Sofresid. 79. Kalman, M., et al., Composite Armored Flexible Riser System for Oil Export Service, in Offshore Technology Conference. 1999: Texas, USA. 80. Hanonge, D., G. Bernard, and A.T. Do, Carbon Fiber Armors Applied to Presalt Flexible Pipe Developments. 2013, Offshore Technology Conference. 81. Kulshreshtha, A.K. and C. Vasile, Advanced Composites for Offshore Developments, in Handbook of Polymer Blends and Composites. 2002, Smithers Rapra Technology. 82. Sontag, T., et al., Chapter 7 - Recent advances in 3D braiding technology, in Advances in 3D Textiles, X. Chen, Editor. 2015, Woodhead Publishing. p Douglass, W.A., Braiding and Braiding Machinery. 1964: Centrex Publishing Company; Cleaver-Hume Press. 167

169 Bibliography 84. Branscomb, D., D. Beale, and R. Broughton, New Directions in Braiding. Journal of Engineered Fibres and Fabrics, (2): p Ma, G., D.J. Branscomb, and D.G. Beale, Modeling of the tensioning system on a braiding machine carrier. Mechanism and Machine Theory, : p Omeroglu, S., The Effect of Braiding Parameters on the Mechanical Properties of Braided Ropes. Fibre & Textiles in Eastern Europe, (4): p Zhang, Q., D. Beale, and R.M. Broughton, Analysis of Circular Braiding Process, Part 1: Theoretical Investigation of Kinematics of the Circular Braiding Process. Journal of Manufacturing Science and Engineering, (3): p Cox, B.N. and G. Flanagan, Handbook on Analystical methods for textiles composites. 1997, National Aeronautics and Space Adminsitration: Hampton, Virginia. 89. TexGen, TexGen : University of Nottingham, United Kingdom. 90. Zhang, Q., et al., Structural Analysis of a Two- dimensional Braided Fabric Journal of Textile Institute, (1): p Potluri, P., et al., Geometrical modelling and control of a triaxial braiding machine for producing 3D preforms. Composites Part A: Applied Science and Manufacturing, (6): p Claes, L., et al., The influence of various carbon fibre braiding techniques and methods of fixation on the extensibility of ligament prosthesis. Biomaterials, : p Phoenix, S.L., Mechanical response of a Tubular Braided Cable with an Elastic Core. Textile Research Journal, (2): p Harte, A.-M. and N. Fleck, On the mechanics of braided composites in tension. European Journal of Mechanics - A/Solids, (2): p Pickett, A.K. and M.R.C. Fouinneteau, Material characterisation and calibration of a meso-mechanical damage model for braid reinforced composites. Composites Part A: Applied Science and Manufacturing, (2): p Tate, J., A. Kelkar, and J. Whitcomb, Effect of braid angle on fatigue performance of biaxial braided composites. International Journal of Fatigue, (10): p Naik, R.A., P.G. Ifju, and J.E. Masters, Effect of fiber architecture parameters on deformation fields and elastic moduli of 2-D braided composites. Journal of Composite Materials, (7): p Charlebois, K.M., et al., Evaluation of the Physical and Mechanical Properties of Braided Fabrics and their Composites. Journal of Reinforced Plastics and Composites, (14): p

170 Bibliography 99. Brunnschweiler, D., The Structure and Tensile Properties of Braids. Journal of the Textile Institute Transactions, (1): p. T55-T West, A.C. and D.O. Adams, Axial Yarn Crimping Effects in Braided Composite Materials. Journal of Composite Materials, : p Gu, H. and Z. Zhili, Tensile behavior of 3D woven composites by using different fabric structures. Materials & Design, (7): p Kumar, S. and Y. Wang, Composites Engineering Handbook. 1997, New York: Inc., Marcel Dekker Rawal, A., H. Saraswat, and A. Siba, Tensile response of braided structures: a review. Textile Research Journal, 2005: p Rawal, A., et al., Geometrically controlled tensile response of braided sutures. Materials Science and Engineering: C, : p Ahmadi, M.S., et al., An experimental study on mechanical properties of GFRP braid-pultruded composite rods. express Polymer Letters, (9): p Pawlowicz, A., et al., Method and device for continuous formation of braid reinforced thermoplastic structural and flexible members Head, A.A., D. Lambert, and J. Peter, Pultrusion method and device for forming composites using pre-consolidated braids Gautam, M., et al., Hybrid composite wires for tensile armours in flexible risers: Manufacturing and mechanical characterisation. Composite Structures, : p ASTM, Standard Test Methods for Constituent Content of Composite Materials - D , Annual Book of ASTM Standards Li, Y., Q. Li, and H. Ma, The voids formation mechanisms and their effects on the mechanical properties of flax fiber reinforced epoxy composites. Composites Part A: Applied Science and Manufacturing, : p Haj-Ali, R. and H. Kilic, Nonlinear behavior of pultruded FRP composites. Composites Part B: Engineering, (3): p Bezdek, A. and W. Kuperberg, Maximum density Space Packing with Conguent Circular Cylinders of Infinite Length Mathematika, (1238): p Starostin, E.L., On the perfect hexagonal packing of rods. Journal of Physics: Condensed Matter, (14): p. S187-S ISO, Textiles -- Woven fabrics -- Construction -- Methods of analysis -- Part 3: Determination of crimp of yarn in fabric - ISO : Stuart, I.M., Capstan equation for strings with rigidity. British Journal of Applied Physics, (10): p ASTM, Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials - D

171 Bibliography 117. ASTM, Standard Test Method for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending - D : Annual Book of ASTM Standards ASTM, Flexural Properties of Polymer Matrix Composite Materials - D7264/D7264M. 2007, Annual Book of ASTM Standards ISO, Fibre-reinforced plastic composites -- Determination of flexural properties -ISO BSI, Methods of testing plastics. Glass reinforced plastics. Determination of flexural properties. Three point method BS :Method ASTM, Standard Test Method for Flexural Properties of Fiber Reinforced Pultruded Plastic Rods - D , Annual Book of ASTM Standards OriginLab, Origin version , Northampton, Massachusetts ASTM, Standard Test Method for Tensile Properties of Pultruded Glass- Fiber-Reinforced Plastic Rod - D , Annual Book of ASTM Standards Rivin, E., Stiffness and Damping in Mechanical Design. 1999: CRC Press ASTM, Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a ± 45 Laminate - D 3518/D 3518M 2001, Annual Book of ASTM Standards ASTM, Standard Test Method for Inplane Shear Properties of Hoop Wound Polymer Matrix Composite Cylinders - D5448/D , Annual Book of ASTM Standards J.C.Halpin and S.W.Tsai, Environmental Factors in Composite Design DSM, Dyneema high-strength, high-modulus polyethylene fiber SK 78, D. Brand, Editor Chocron, S., et al., Modelling of fabric impact with high speed imaging and nickel-chromium wires vaildation, in 26th International Symposium on Ballistics. 2011: Miami, Florida Hagstrand, P.O., F. Bonjour, and J.A.E. Månson, The influence of void content on the structural flexural performance of unidirectional glass fibre reinforced polypropylene composites. Composites Part A: Applied Science and Manufacturing, (5): p Pipes, R.B. and N.J. Pagano, Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension. Journal of Composite Materials, : p Potluri, P., et al., Flexural and torsional behaviour of biaxial and triaxial braided composite structures. Composite Structures, (1 4): p Franssen, J.-M. and P.V. Real, Annex C: Mechanical Properties of Carbon Steel and Stainless Steel, in Fire Design of Steel Structures. 2010, Wiley-VCH Verlag GmbH & Co. KGaA. p

172 Bibliography 134. Collins, J.A., H. Busby, and G. Staab, Chapter 3 - Materials Selection, in Mechanical Design of Machine Elements and Machines Witz, J.A., A Case Study in the Cross-section Analysis of Flexible Risers. Marine Structures, : p Dhiman, S., P. Potluri, and C. Silva, Influence of binder configuration on 3D woven composites. Composite Structures, : p Kandelbauer, A., et al., Unsaturated Polyesters and Vinyl Esters. Third Edit ed. 2014: Elsevier Inc Nakanishi, Y., K. Matsumoto, and Y. Yamada. Damping behaviour of woven fabric composites. in Proceedings of the sixth joint Canada-Japan workshop on composites Toronto: DEStech Publication Hull, D. and T.W. Clyne, An Introduction to Composite Materials. Second ed. 1996: Cambridge University Press J.F.Nye, Physical Properties of Crystals - Their Representaion by Tensors and Matrices. 1985: Clarendon Oxford Clyne, T.W., A compressibility-based derivation of simple expressions for the transverse Poisson's Ratio and shear modulus of an alihned long fibre composite. Journal of Material Science and Letters, : p Summerscales, J., The bulk modulus of carbon fibres. Journal of Materials Science Letters, (1): p Rawal, a., R. Kumar, and H. Saraswat, Tensile mechanics of braided sutures. Textile Research Journal, (16): p Rawal, A., H. Saraswat, and R. Kumar, Tensile response of tubular braids with an elastic core. Composites Part A: Applied Science and Manufacturing, : p Del Rosso, S., L. Iannucci, and P.T. Curtis, Experimental investigation of the mechanical properties of dry microbraids and microbraid reinforced polymer composites. Composite Structures, : p Hopper, R.H., J.W. Grant, and P. Popper, Mechanics of a Hybrid Circular Braid with an Elastic Core. Textile Research Journal, (12): p Hristov, K., et al., Mechanical Behavior of Circular Hybrid Braids Under Tensile Loads. Textile Research Journal, (1): p Byun, J.-H., The analytical characterization of 2-D braided textile composites. Composites Science and Technology, (5): p Prtitchard, G., An introduction to plastics for non-specialists. Reinforced Plastics Durability, ed. G. Prtitchard. 1999, Cambridge, England: Woodhead Publishing Limited Kennedy, A. and P. Shipway, Chapter 2 : Materials and processing, in An Introduction to Mechanical Engineering - Part 1, M. Clifford, et al., Editors. 2006, CRC Press. 171

173 Bibliography 151. Martiienssen, W. and H. Warlimont, Chapter Polymers, in Springer Handbook of Condensed Matter and Materials Data, W. Martiienssen and H. Warlimont, Editors. 2005, Springer Kurtz, S.M., Chapter 1- A Primer on UHMWPE, in UHMWPE Biomaterials Handbook (Third Edition). 2016, William Andrew Publishing: Oxford. p Mathworks, MATLAB version R2014a. 2014: Natick, Massachusetts Zhou, Y., X. Chen, and G. Wells, Influence of yarn gripping on the ballistic performance of woven fabrics from ultra-high molecular weight polyethylene fibre. Composites Part B: Engineering, : p Simulia, Abaqus version : Vélizy-Villacoublay, France Simulia, ABAQUS: Theory Manual Hannemann, M.M., Shelling Hexahedral Complexes for Mesh Generation. Journal of Graph Algorithm and Applications, (5): p Schonning, A., et al., Hexahedral mesh development of free-formed geometry: The human femur exemplified. Computer-Aided Design, (8): p Benzley S.E, et al., A comparison of all-hexahedral and all-tetrahedral finite element meshes for elastic and elasto-plastic analysis, in International meshing Roundtable. 1995: Sandia National Laboratories. p Vautard, F., L. Xu, and L.T. Drzal, Carbon Fiber Vinyl Ester Interfacial Adhesion Improvement by the Use of an Epoxy Coating, in Major Accomplishments in Composite Materials and Sandwich Structures, I.M. Daniel, E.E. Gdoutos, and Y.D.S. Rajapakse, Editors. 2010, Springer Netherlands: Dordrecht. p Banerjee, A., et al., Model and experimental study of fiber motion in wet filament winding. Composites Part A: Applied Science and Manufacturing, (3): p Roy, S.S., W. Zao, and P. Potluri, Influence of Braid Carrier Tension on Carbon Fibre Braided Preforms, in Recent Developments in Braiding and Narrow Weaving, Y. Kyosev, Editor. 2016, Springer International Publishing: Cham. p Garoushi, S., L.V.J. Lassila, and P.K. Vallittu, The effect of span length of flexural testing on properties of short fiber reinforced composite. Journal of Materials Science: Materials in Medicine, (2): p Shan, H.-Z. and T.-W. Chou, Transverse elastic moduli of unidirectional fiber composites with fiber/matrix interfacial debonding. Composites Science and Technology, (4): p ISO, Petroleum and natural gas industries -- Design and operation of subsea production systems -- Part 5: Subsea umbilicals - ISO , ISO. p

174 Bibliography 166. Kriz, R.D. and W.W. Stinchcomb, Elastic moduli of transversely isotropic graphite fibers and their composites. Experimental Mechanics, (2): p

175 Appendix Appendix In this section of thesis, following points from the thesis have been explained: Braiding using 12 and 24 carriers on a 24 carriers braiding machine for bundled rod with Ф 2 mm rods Derivation of cover factor equation for over-braid sleeve in hybrid composite wires Calculation of volume of biaxial tow and total volume of unit cell for braid shell properties quantification MATLAB script for analytical prediction of elastic properties of braid shell Technical data-sheet for Dyneema fibres 174

176 Appendix A.1: Braiding using 12 and 24 carriers on a 24 carriers braiding machine for bundled rods with Ф 2 mm rods. (a) (b) (c) (d) Figure A. 1: Braiding of hexagonally packed rods with Φ 2 mm rods: (a) & (b) using 12 carriers, and (c) & (d) using 24 carriers. 175

177 Appendix A.2: Derivation of braid angle for over-braid sleeve The quantification of braid angle for biaxial over-braid sleeve to suit the cross-section of the hybrid composite wires, has been derived from the Eq. (A. 1) already present in literature [91], that quantifies the braid angle (θ) for core with circular cross-section, using core diameter (R), the rotational speed (ω), and linear take-up speed (v). θ = tan -1 ( Rω v ) (A. 1) 2πR = 6 ( πr 3 ) + 6(2r) (A. 2) R = (r + 6r π ) θ hcw = tan -1 rπ + 6r [( ) ( ω (A. 3) π v )] The braid angle for biaxial over-braid sleeve (θ hcw ) can be quantified with the help of Eq. (A. 3), where r is the individual rod diameter. This equation has been obtained by substituting the determining equivalent value of R in Eq. (A. 2). The perimeter of a circular core (2πR) has been assumed to be same as the perimeter [6 ( πr 3 ) + 6(2r)] that over-braid sleeve covers around the bundled rods. 176

178 Appendix A.3: Derivation of cover factor for biaxial over-braid sleeve The quantification of cover factor (Cf) for circular over-braid sleeves on a structure with geometrical cross-section has been depicted in Eq. (A. 4) obtained from [91], that quantifies cover factor using manufacturing parameters such as: the braid angle (θ), mandrel or core diameter (R), number of carriers (Nc), and the tow width (w). C f = 1 - ( 1 2 (A. 4) wn c 4πRcosθ ) The same equation has been used, however modified to suit the cross-section to determine the cover factor of over-braid sleeve on bundled rods using manufacturing parameters. The perimeter of a circular core (2πR) has been assumed to be same as the perimeter [6 ( πr ) + 6(2r)] that over-braid sleeve covers around the bundled rods. 3 2πR = 6 ( πr 3 ) + 6(2r) (A. 5) R = (r + 6r π ) Substituting value of R from Eq. (A. 5) into Eq. (A. 4), the cover factor (Cfhw) for over braid sleeve in the hybrid composite wire can be deduced in form of Eq. (A. 6). Therefore the cover factor (Cfhw) for over-braid sleeve can be quantified using individual rod radius (r) used in the packing, number of carriers (Nc), width of the tow (w), and braid angle (θ). C fhw = 1 - [1 2 (A. 6) wn c 4r(π + 6) cosθ ] 177

179 Appendix A.4: Calculation of volume of biaxial tow and total volume of unit cell for braid shell properties quantification The quantification of volume of biaxial tows in a braid unit cell and the total volume of braid unit cell has been quantified in this section. The analytical equations expressed in this section, are based on following assumptions: The cross-section of the braided tows has been assumed to be elliptical, the fibre volume fraction of fibres in a tow, has been assumed to be 0.70, i.e. similar to the fibre volume fraction used to calculate the stiffness of the tow in Chapter 5 (Pg. 114) The cross-section of the tows has been assumed to be elliptical. It should be noted that these analytical equations only give an approximate solution, since the actual measurement of volume of unit cell of a braid is not practically feasible. Use of X-ray tomography could be employed, the technique is not expected to yield exact results for volume of braid unit cell. In actual cross-section of a fabric, the tows are not expected to be straight as assumed for regular braid unit cell below. A.4.1. Volume of biaxial tows in a diamond braid unit cell and total volume of the unit cell Figure A. 2: Schematic representation of cross-section of biaxial braid with diamond braid topology along the fibre axis, depicting path followed by the tows during undulation In order to calculate the volume of biaxial tows in a diamond braid unit cell, volume of biaxial tows along the undulation paths needs to be determined. The two types of 178

180 Appendix paths followed by braid tows in a diamond braid unit cell have been shown in Figure A. 2. Figure A. 3: Schematic representation of cross-section of biaxial braid with diamond braid topology along the fibre axis, depicting different thicknesses and lengths of tows in a braid The area of the biaxial tow with an elliptical cross-section can be quantified using Eq. (A. 7). Area of biaxial tow = πt tt w 4 (A. 7) Volume of path 1 : The length of the tow in path 1 can be expressed to be equal to half the perimeter of an elliptical cross-sectional tow, it is crossing over or under, which has been depicted in Eq. (A. 8). Length of undulation = π [3 ( t t + t w 2 ) ( 3t t + t w 2 2 ) ( t t + 3t w 2 )] (A. 8) The volume of biaxial tow in path 1 ( V path1 ) can be expressed as Eq. (A. 9) V path1 = π 2 t t t w [3 ( t t + t w 2 ) ( 3t t + t w 2 8 ) ( t t + 3t w 2 )] (A. 9) Since, there are 4 biaxial tows and 8 path 1, in a diamond braid unit cell, the total volume of biaxial tows containing path 1 ( TV path1 ), can be expressed as in Eq. (A. 10). 179

181 Appendix TV path1 = π 2 t t t w [3 ( t t + t w 2 ) ( 3t t + t w 2 ) ( t t + 3t w ) ] 2 (A. 10) Volume of path 2 : For path 2, that consists of a cross-over length, can be quantified using simple geometrical equations, where cross-over length can be expressed as: t s sec ϕ, where t s is inter-tow spacing (see Figure A. 3), and ϕ as crimp angle. The volume of this cross-over length (V path 2 ) will be approximately equal to the expression in Eq. (A. 11) V path 2 = (t s sec ϕ) ( πt tt w 4 ) (A. 11) Since there are 4 cross-over lengths in a diamond braid unit cell, the total volume of cross-over length (TV path 2 ) can be multiplied by 4 and quantified as Eq. (A. 12) TV path 2 = (t s sec ϕ) (πt t t w ) (A. 12) Therefore the total volume of biaxial tows in a diamond braid unit cell can be expressed as the sum of Eq. (A. 10) and Eq. (A. 12), in form of Eq. (A. 13). However, the total volume of biaxial tows (Vb) obtained needs to be multiplied by the fibre volume fraction of V b = [(t s sec ϕ) (πt t t w )] + (A. 13) π 2 t t t w [3 ( t t + t w 2 ) ( 3t t + t w 2 ) ( t t + 3t w ) ] 2 The total volume of braid unit cell (Vt) can be expressed as in Eq. (A. 14), as the sum of area of Δ abc and Δ dbc (in Figure A. 4), where each will have an area of ½ thtu. The sum of these two areas will give a product of thtu. The tb in Eq. (A. 14), is the thickness of the braid. 180

182 Appendix a d th tu b c Figure A. 4: Computer aided representation of braid unit cell with diamond braid topology V t = t b t u t h (A. 14) A.4.2. Volume of biaxial tows in a regular braid unit cell and total volume of unit cell Figure A. 5: Schematic representation of cross-section of biaxial braid with regular braid topology along the fibre axis. In order to calculate the volume of biaxial tows in a regular braid unit cell, volume of biaxial tows along the undulation paths needs to be determined. The three types of paths followed by braid tows in a regular unit cell have been shown in Figure A. 5. The different thicknesses and lengths in a regular braid unit cell has been shown in Figure A. 6. These thicknesses and lengths have been used to compute the volume of biaxial tows in a regular braid unit cell. 181

183 Appendix Figure A. 6: Schematic representation of cross-section of biaxial braid with regular braid topology along the fibre axis Volume of path 1 : The length of path 1 can be determined using image analysis, and by physical measurement (taking average of both measurements). This length of path 1 will be referred here as t l. The volume of tow in path 1 (V path 1 ) has been quantified in Eq. (A. 15), using the area of an ellipse as: πt tt w 4. V path 1 = πt tt w t l 4 (A. 15) There are total 16 path 1 lengths, in a regular braid unit cell (each tow has 2 path 1 and there are 8 tows in unit cell). The total volume of biaxial tows in path 1 has been quantified in Eq. (A. 16). TV path 1 = 4πt t t w t l (A. 16) Volume of path 2 : The length in path 2 consists of cross-over length that can be quantified using simple geometrical equations, where cross-over length can be expressed as: t s sec ϕ, where t s is the inter-tow spacing (see Figure A. 6), and ϕ is the crimp angle. The volume of this cross-over length (V path 2 ) will be approximately equal to the expression in Eq. (A. 17). V path 2 = (t s sec ϕ) ( πt tt w 4 ) (A. 17) Since there are 12 cross-over lengths in a regular braid unit cell, the total volume of cross-over length (TV path 2 )can be multiplied by 12 and quantified as Eq. (A. 18). 182

184 Appendix TV path 2 = (t s sec ϕ) (3πt t t w ) (A. 18) Volume of path 3 : The path 3 is the curved length of the tow, and its length can be quantified as ¼ th of the perimeter of an ellipse. The length of this path (L path 3 ) has been quantified in Eq. (A. 19). L path 3 = π [3 ( t t + t w 2 ) ( 3t t + t w 2 4 ) ( t t + 3t w 2 )] (A. 19) As there are 32 such lengths (4 in each tow and total of 8 tows in unit cell), the total lengths of biaxial tows in path 3 (TL path 3 ) can be expressed in form of Eq. (A. 20). TL path 3 = 8π [3 ( t t + t w 2 ) ( 3t t + t w 2 ) ( t t + 3t w )] 2 (A. 20) The total volume of the biaxial tow in length path 3 has been expressed as Eq. (A. 21). TV path 3 = 8π 2 t t t w [3 ( t t + t w 2 ) ( 3t t + t w 2 ) ( t t + 3t w )] 2 (A. 21) Therefore, adding Eqs. (A. 16), (A. 18), and (A. 21), the total volume of biaxial braid tows (Vb) in a regular braid unit cell has been expressed in Eq. (A. 22), however the total volume of biaxial tows obtained needs to be multiplied by the fibre volume fraction of 0.70: V b = (t s sec ϕ) (3πt t t w ) + 4πt t t w t l + 8π 2 t t t w [3 ( t t+ t w ) 2 (A. 22) ( 3t t+ t w 2 ) ( t t+ 3t w )] 2 183

185 Appendix The total volume of braid unit cell can be expressed as in Eq. (A. 23), as the sum of area of Δ abc and Δ dbc in Figure A. 7, where each will have an area of ½ thtu. The sum of these two areas will give a product of thtu. Figure A. 7: Computer aided representation of braid unit cell with regular braid topology V t = t b t u t h (A. 23) From the Eqs (A. 13), (A. 14), (A. 22), and (A. 23), the volume of biaxial tows and total volume of unit cell for a biaxial over-braid sleeve has been calculated and reported in Table A.1. Table A.1: Values of Va and Vb for calculation of braid shell properties Type Topology Braid angle ( ) Vb Vt 1 1/ / / / / / The volume of biaxial tows can also be calculated in a simpler manner as well, first by determining the braid cover and multiplying it with overall thickness of the braid to achieve an approximate solution. 184

186 Appendix A.5: MATLAB script for analytical prediction of elastic properties of braid shell: %Quantification of braid shell properties% clc; clear; %Elastic properties of fibres and matrix inside tow% f=0.70; %Fibre volume fraction inside the tow% phi=0.25; %Crimp angle in radians% thetap=30; %braid angle with positive theta% thetam=-30; %braid angle with minus theta% Em=0.7; %Young s modulus of High density polyethylene matrix as weak matrix% % Obtained from literature% Ef=116; % Axial modulus of Dyneema fibres% % Obtained from technical data sheet% Gf=0.95; %Young s modulus of Dyneema fibres% Gm=0.25; %shear modulus of High density polyethylene matrix% v12f=0.29; %Fibre Poisson's ratio% E22f=3; %Fibre transverse modulus, obtained from technical data sheet% v21f=(e22f*v12f)/ef; %Calculated% v23f=0.2; %Obtained from literature% q1=(ef*e22f*e22f)^1/3; q2=(v12f*v12f*v23f)^1/3; Kf=(q1)/(3*(1-2*q2)); %Bulk modulus for orthotropic fibres% vm=0.40; %%Matrix Poisson's ratio obtained from literature%% a=3*(1-2*vm); Km=Em/a;%%Obtained from literature%% Vt=11.5; %Experimentally and analytically determined%% Vb=8.5; %Experimentally and analytically determined %% % % % Tow property calculation % % % E11=(1-f)*Em+f*Ef; fac = 2.0; ita =((Ef/Em)-1)/((Ef/Em)+fac); p1=(1+(fac*ita*f)); p2=(1-(ita*f)); E22=Em*(p1/p2); %Calculated using Halpin & Tsai equations% K=((f/Kf)+((1-f)/Km))^-1; v12=f*v12f+(1-f)*vm; v21=(v12*e22)/e11; h=3*k; v23=1-v21-(e22/h); v32=v23; facs=1; itas=((gf/gm)-1)/((gf/gm)+facs); p1s=(1+(facs*itas*f)); p2s= (1-(itas*f)); 185

187 Appendix G12=Gm*(p1s/p2s); %Calculated using Halpin & Tsai equations% j=2*(1+v23); G23=E22/j; G32=G23; % % % Formulation of compliance matrix [166] in the coordinate system % % % S = [ 1/E11, -v21/e22, -v21/e22, 0, 0, 0; -v12/e11, 1/E22, -v32/e22, 0, 0, 0; -v12/e11,-v23/e22, 1/E22, 0, 0, 0; 0, 0, 0, 1/G23, 0, 0; 0, 0, 0, 0, 1/G12, 0; 0, 0, 0, 0, 0, 1/G12]; % % % Incorporating crimp angle in stiffness matrix % % % m=cos(phi); n=sin(phi); Tc=[(m^2),0,(n^2),0,-2*m*n, 0; 0,1,0,0,0,0; (n^2),0,(m^2),0,2*m*n,0; 0, 0,0,m,0,n; m*n, 0,-m*n,0,((m^2)-(n^2)),0; 0, 0,0,-n,0,m]; S_ct=Tc'*S*Tc; % ' stands for transpose matrix% % % % Calculation of U matrix % % % U1=((3*S_ct(1,1))+(3*S_ct(3,3))+(2*S_ct(1,3))+(S_ct(5,5)))/8; U2=(S_ct(1,1)-S_ct(3,3))/2; U3=(S_ct(1,1)+S_ct(3,3)-(2*S_ct(1,3))-S_ct(5,5))/8; U4=(S_ct(1,1)+S_ct(3,3)+(6*S_ct(1,3))-S_ct(5,5))/8; U5=(S_ct(1,1)+S(3,3)-(2*S_ct(1,3))+S_ct(5,5))/8; U6=(S_ct(1,2)+S_ct(3,2))/2; U7=(S_ct(1,2)-S_ct(3,2))/2; U8=(S_ct(4,4)+S_ct(6,6))/2; U9=(S_ct(4,4)-S_ct(6,6))/2; %Formulation of the effective compliance [S(c)] matrix of a crimped yarn% %in the x'-y-z co-ordinate system (crimp angle=phi)% z=2*phi; n=4*phi; r=sin(z); s=sin(n); t=sin(phi); S11c=U1+((U2/z)*r)+((U3/n)*s); 186

188 Appendix S12c=U6+(U7/z)*r; S13c=U4-(U3/n)*s; S14c=0; S15c=-((U2*t*t)+(U3*r*r))/phi; S16c=0; S21c=S12c; S22c=S(2,2); S23c=U6-((U7/z)*r); S24c=0; S25c=-(2*U7/phi)*t*t; S26c=0; S31c=S13c; S32c=S23c; S33c=U1-((U2/z)*r)+((U3/n)*s); S34c=0; S35c=-((U2*t*t)-(U3*r*r))/phi; S36c=0; S41c=S14c; S42c=S24c; S43c=S34c; S44c=U8+((U9/z)*r); S45c=0; S46c=(U9/n)*t*t; S51c=S15c; S52c=S25c; S53c=S35c; S54c=S45c; S55c=4*U5-((U3/phi)*s); S56c=0; S61c=S16c; S62c=S26c; S63c=S36c; S64c=S46c; S65c=S56c; S66c=U8-((U9/z)*r); S_c = [S11c,S12c,S13c,S14c,S15c,S16c; S21c,S22c,S23c,S24c,S25c,S26c; S31c,S32c,S33c,S34c,S35c,S36c; S41c,S42c,S43c,S44c,S45c,S46c; S51c,S52c,S53c,S54c,S55c,S56c; S61c,S62c,S63c,S64c,S65c,S66c]; % % %Formulation of effective compliance matrix [S(b)] in the x'-y-z% %co-ordinate system% % % %Braid angle (positive)% p=cosd(thetap); q=sind(thetap); Tb=[(p^2),(q^2),0,0,0, 2*p*q; q^2, p^2,0,0,0,-2*p*q; 0, 0,1,0,0, 0; 0, 0,0,p, -q,0; 0, 0,0,q, p,0; 187

189 Appendix -p*q, p*q,0,0,0,p^2-q^2]; Sb_p=Tb'*S_c*Tb; % ' stands for transpose matrix' %Braid angle (negative)% p=cosd(thetam); q=sind(thetam); Tb=[(p^2),(q^2),0,0,0, 2*p*q; q^2, p^2,0,0,0,-2*p*q; 0, 0,1,0,0, 0; 0, 0,0,p, -q,0; 0, 0,0,q, p,0; -p*q, p*q,0,0,0,(p^2)-(q^2)]; Sb_m=Tb'*S_c*Tb; % % %Formulation of stiffness matrices% % % Cb_p = inv(sb_p); Cb_m = inv(sb_m); % % %Formulation of the effective stiffness and compliance matrix% % % C_eff= ((Cb_p)*((Vb)/(2*Vt)))+((Cb_m)*((Vb)/(2*Vt))); S_eff=inv(C_eff); % % %Calculation of the effective properties% % % Exx=1/S_eff(1,1); Eyy=1/S_eff(2,2); Ezz=1/S_eff(3,3); Gyz=1/S_eff(4,4); Gxz=1/S_eff(5,5); Gxy=1/S_eff(6,6); vxy=-s_eff(1,2)/s_eff(1,1); vzx=-s_eff(1,3)/s_eff(3,3); vyz=-s_eff(2,3)/s_eff(2,2); 188

190 Appendix A.6: Technical data-sheet for Dyneema fibres 189